CHAPTER
TRUE/FALSE
1.Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities. They cannot be used when making decisions about investments in physical assets.
ANS: F 
DIF: Easy 
TOP: Cash flow time lines 
2.One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest.
ANS: T 
DIF: Easy 
TOP: Retirement and compounding 
3.Of all the techniques used in finance, the least important is the concept of the time value of money.
ANS: F 
DIF: Easy 
TOP: Time value concepts 
4.Compounding is the process of converting today's values, which are termed present value, to future value.

ANS: T 
DIF: 
Easy 
TOP: Compounding 
5. 
The coupon rate is the rate of return you could earn on alternative investments of similar risk. 


ANS: F 
DIF: 
Easy 
TOP: Coupon rate 
6. 
A perpetuity is an annuity with perpetual payments. 


ANS: T 
DIF: 
Easy 
TOP: Perpetuity 
7.An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt.
ANS: T 
DIF: Easy 
TOP: Amortization 
8.The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.
ANS: F 
DIF: Medium 
TOP: Compounding 
9.Suppose an investor can earn a steady 5% annually with investment A, while investment B will yield a constant 12% annually. Within 11 years time, the compounded value of investment B will be more than twice the compounded value of investment A (ignore risk).
ANS: T 
DIF: Medium 
TOP: Comparative compounding 
10.Solving for the interest rate associated with a stream of uneven cash flows, without the use of a calculator, usually involves a trial and error process.
ANS: T 
DIF: Medium 
TOP: Uneven cash flows and interest 
Chapter 4 ï The Time Value of Money 39
11.When a loan is amortized, the largest portion of the periodic payment goes to reduce principal in the early years of the loan such that the accumulated interest can be spread out over the life of the loan.
ANS: F 
DIF: Medium 
TOP: Amortization 
12.The effective annual rate is always greater than the simple rate as a result of compounding effects.
ANS: F 
DIF: Medium 
TOP: Effective and simple rates 
13.Because we usually assume positive interest rates in time value analyses, the present value of a
ANS: F 
DIF: Medium 
TOP: Lump sum and annuity 
14.All else equal, a dollar received sooner is worth more than a dollar received at some later date, because the sooner the dollar is received the more quickly it can be invested to earn a positive return.
ANS: T 
DIF: Medium 
TOP: Time value concepts 
15.An annuity is a series of equal payments made at fixed
ANS: T 
DIF: Medium 
TOP: Annuities 
16.The difference between an ordinary annuity and an annuity due is that each of the payments of the annuity due earns interest for one additional year (period).
ANS: T 
DIF: Medium 
TOP: Annuities 
17.The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.
ANS: T DIF: Medium TOP: Annuities
18. The effective annual rate is less than the simple rate when we have monthly compounding. ANS: F DIF: Medium TOP: Effective annual rate
MULTIPLE CHOICE
1.Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will
a.Be higher.
b.Be lower.
c.Stay the same.
d.Cannot tell.
e.Be variable.
ANS: B 
DIF: Easy 
OBJ: TYPE: Conceptual TOP: PV of a sum 
2.You have determined the profitability of a planned project by finding the present value of all the cash flows form that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?
40Chapter 4 ï The Time Value of Money
a.The discount rate decreases.
b.The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
c.The discount rate increases.
d.Answers b and c above.
e.Answers a and b above.
ANS: 
A 
DIF: Easy 
OBJ: TYPE: Conceptual 
TOP: 
PV and discount rate 

3.As the discount rate increases without limit, the present value of the future cash inflows
a.Gets larger without limit.
b.Stays unchanged.
c.Approaches zero.
d.Gets smaller without limit, i.e., approaches minus infinity.
e.Goes to ern.
ANS: 
C 
DIF: Easy 
OBJ: TYPE: Conceptual 
TOP: 
PV and discount rate 

4.Which of the following statements is most correct?
a.If annual compounding is used, the effective annual rate equals the simple rate.
b.If annual compounding is used, the effective annual rate equals the periodic rate.
c.If a loan has a 12 percent simple rate with semiannual compounding, its effective annual rate is equal to 11.66 percent.
d.Both answers a and b are correct.
e.Both answers a and c are correct.
ANS: D
Statement d is correct. The equation for EAR is as follows:
If annual compounding is used, m = 1 and the equation above reduces to EAR = rSIMPLE. The equation for the periodic rate is:
If annual compounding is used then m = 1 and rPER = rSIMPLE and since EAR = rSIMPLE then rPER = EAR.
DIF: Easy OBJ: TYPE: Conceptual TOP: Effective annual rate
5.Why is the present value of an amount to be received (paid) in the future less than the future amount?
a.Deflation causes investors to lose purchasing power when their dollars are invested for greater than one year.
b.Investors have the opportunity to earn positive rates of return, so any amount invested today should grow to a larger amount in the future.
c.Investments generally are not as good as those who sell them suggest, so investors usually are not willing to pay full face value for such investments, thus the price is discounted.
d.Because investors are taxed on the income received from investments they never will buy an investment for the amount expected to be received in the future.
e.None of the above is a correct answer.
ANS: 
B 
DIF: Easy 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

Chapter 4 ï The Time Value of Money 41
6.By definition, what type of annuity best describes payments such as rent and magazine subscriptions (assuming the costs do not change over time)?
a.ordinary annuity
b.annuity due
c.nonconstant annuity
d.annuity in arrears
ANS: B 
DIF: Easy 
OBJ: TYPE: Conceptual TOP: Annuities 
7.What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually?
a.equal to 10 percent
b.greater than 10 percent
c.less than 10 percent
d.This question cannot be answered without knowing the dollar amount of the investment.
e.None of the above is correct.
ANS: 
A 
DIF: Easy 
OBJ: TYPE: Conceptual 
TOP: 
Effective annual rate 

8.What is the term used to describe an annuity with an infinite life?
a.perpetuity
b.infinuity
c.infinity due
d.There is no special term for an infinite annuity.
ANS: A 
DIF: Easy 
OBJ: TYPE: Conceptual TOP: Perpetuity 
9.Everything else equal, which of the following conditions will result in the lowest present value of an amount to be received in the future?
a.annual compounding
b.quarterly compounding
c.monthly compounding
d.daily compounding
ANS: 
D 
DIF: Easy 
OBJ: TYPE: Conceptual 
TOP: 
PV and effective annual rate 

10.Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational
a.The annuity due.
b.The deferred annuity.
c.Either one, because as the problem is set up, they have the same present value.
d.Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better.
e.The annuity due; however, if the payments on both were doubled to $10,000, the deferred annuity would be preferred.
ANS: A 
DIF: Medium 
OBJ: TYPE: Conceptual TOP: Annuities 
42Chapter 4 ï The Time Value of Money
11.Which of the following statements is correct?
a.For all positive values of k and n, FVIFr, n 1.0 and PVIFAr, n n.
b.You may use the PVIF tables to find the present value of an uneven series of payments. However, the PVIFA tables can never be of use, even if some of the payments constitute an annuity (for example, $100 each year for Years 3, 4, and 5), because the entire series does not constitute an annuity.
c.If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective annual rate.
d.The present value of a future sum decreases as either the simple interest rate or the number of discount periods per year increases.
e.All of the above statements are false.
ANS: 
D 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

12.Which of the following statements is correct?
a.Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity.
b.Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future.
c.The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment.
d.There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other).
e.Each of the above statements is true.
ANS: 
C 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

13.A $10,000 loan is to be amortized over 5 years, with annual
a.The annual payments would be larger if the interest rate were lower.
b.If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the
c.The last payment would have a higher proportion of interest than the first payment.
d.The proportion of interest versus principal repayment would be the same for each of the 5 payments.
e.The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.
ANS: E
If the interest rate were higher, the payments would all be higher, and all of the increase would be attributable to interest. So, the proportion of each payment that represents interest would be higher.
Note that statement b is false because interest during Year 1 would be the interest rate times the beginning balance, which is $10,000. With the same interest rate and the same beginning balance, the Year 1 interest charge will be the same, regardless of whether the loan is amortized over 5 or 10 years.
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: Time value concepts 
Chapter 4 ï The Time Value of Money 43
14.Which of the following statements is correct?
a.Simple rates can't be used in present value or future value calculations because they fail to account for compounding effects.
b.The periodic interest rate can be used directly in calculations as long as the number of payments per year is greater than or equal to the number of compounding periods per year.
c.In all cases where interest is added or payments are made more frequently than annually, the periodic rate is less than the annual rate.
d.Generally, the APR is greater than the EAR as a result of compounding effects.
e.If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by two.
ANS: 
C 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Types of interest rates 

15.All else equal, if you expect to receive a certain amount in the future, say, $500 in ten (10) years, the present value of that future amount will be lowest if the interest earned on such investments is compounded
a.daily
b.weekly
c.monthly
d.quarterly
e.annually
ANS: 
A 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

16.Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments.
a.rent payments associated with a
b.payments for a magazine subscription for a
c.interest payments associated with a corporate bond that was issued today
d.annual payments associated with lottery winnings that are paid out as an annuity
ANS: C 
DIF: Medium 
OBJ: TYPE: Conceptual TOP: Annuities 
17.All else equal, the future value of a
a.interest rate that is earned is lowered.
b.number of compounding periods is increased.
c.investment time period is shortened.
d.amount initially invested is lowered.
e.Two or more of the above answers are correct.
ANS: 
B 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

18.Susan just signed a
a.ordinary annuity
b.annuity due
c.series of uneven cash flows
d.perpetuity
ANS: B 
DIF: Medium 
OBJ: TYPE: Conceptual TOP: Annuities 
44Chapter 4 ï The Time Value of Money
19.Suppose that the present value of receiving a guaranteed $450 in two years is $385.80. The opportunity rate of return on similar risk investments is 8 percent. According to this information, all else equal, which of the following statements is correct?
a.It always would be preferable to wait two years to receive the $450 because this value is greater than the present value.
b.Risk averse investors always would prefer to take the $385.80 today because it is a guaranteed amount whereas there is uncertainty as to whether the future amount will be paid.
c.No investor should be willing to pay more than $385.80 for such an investment.
d.It is apparent the present value was computed incorrectly because the present value of a future amount always should be greater than the future value.
e.None of the above is a correct answer.
ANS: 
C 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

20.You plan to invest an amount of money in
a.$4,678.82
b.$4,823.13
c.$13,600.00
d.$14,979.90
e.$7,589.29
ANS: 
A 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
PV of a lump sum 

21.Vegit Corporation needs to borrow funds to support operations during the summer. Vegit's CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia. The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments. Which bank should Vegit use for the loan?
a.Bank of Georgia, because the 12 percent simple interest is cheaper than the 12.5 percent simple interest at Bank of Florida.
b.Bank of Georgia, because the effective interest rate on the loan is less than 12 percent, whereas the effective interest rate on the loan at the Bank of Florida is greater than 12.5 percent.
c.Bank of Florida, because the simple interest rate is higher, which means that Vegit will be able to invest the proceeds from the loan at a higher rate of return.
d.Bank of Florida, because the effective interest rate on the loan is 12.5 percent, which is less than the 12.7 percent effective interest rate on the loan offered by the Bank of Georgia.
e.There is not enough information to answer this question.
ANS: 
D 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Effective annual rate 

Chapter 4 ï The Time Value of Money 45
22.Alice's investment advisor is trying to convince her to purchase an investment that pays $250 per year. The investment has no maturity; therefore the $250 payment will continue every year forever. Alice has determined that her required rate of return for such an investment should be 14 percent and that she would hold the investment for 10 years and then sell it. If Alice decides to buy the investment, she would receive the first $250 payment one year from today. How much should Alice be willing to pay for this investment?
a.$1,304.03, because this is the present value of an ordinary annuity that pays $250 a year for 10 years at 14 percent.
b.$1,486.59, because this is the present value of an annuity due that pays $250 a year for 10 years at 14 percent.
c.$1,785.71, because this is the present value of a $250 perpetuity at 14 percent.
d.There is not enough information to answer this question, because the selling price of the investment in 10 years is not known today.
e.None of the above is correct.
ANS: C 
DIF: Medium 
OBJ: TYPE: Conceptual TOP: Perpetuity 
23.At approximately what rate would you have to invest a
a.20%
b.12%
c.24%
d.Not enough information is provided to answer the question.
e.None of the above is a correct answer.
ANS: 
A 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

24.Sarah is thinking about purchasing an investment from HiBond Investing. If she buys the investment, Sarah will receive $100 every three months for five years. The first $100 payment will be made as soon as she purchases the investment. If Sarah's required rate of return is 16 percent, to the nearest dollar, how much should she be willing to pay for this investment?
a.$1,359
b.$1,413
c.$1,112
d.$1,519
e.$1,310
ANS: 
B 
DIF: Medium 
OBJ: TYPE: Conceptual 
TOP: 
PV of an annuity 

25.Which of the following statements is most correct?
a.The first payment under a
b.If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual payments. However, as a borrower you should prefer the annual payment loan.
c.The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero.
d.Statements a, b, and c are all true.
e.Only statements b and c are true.
ANS: 
D 
DIF: Tough 
OBJ: TYPE: Conceptual 
TOP: 
Time value concepts 

46Chapter 4 ï The Time Value of Money
26.A recent advertisement in the financial section of a magazine carried the following claim: "Invest your money with us at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine." Ignoring taxes, how long would it take to double your money at
asimple rate of 14 percent, compounded annually?
a.Approximately 3.5 years
b.Approximately 5 years
c.Exactly 7 years
d.Approximately 10 years
e.Exactly 14 years
ANS: B
Tabular solution:
$1 (FVIF14%, n) = $2 FVIF14%, n = 2.000 n = 5+ years.
Financial calculator solution: Inputs: I = 14; PV =
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Time for a sum to double 
27.At an effective annual interest rate of 20 percent, how many years will it take a given amount to triple in value? (Round to the closest year.)
a.5
b.8
c.6
d.10
e.9
ANS: C
Cash flow time line:
Tabular solution:
$1 = $3 (PVIF20%, n) PVIF20%, n = 0.3333 n = 6 periods (years).
Financial calculator solution: Inputs: I = 20; PV =
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Time for a sum to triple 
Chapter 4 ï The Time Value of Money 47
28.You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?
a.$1,171
b.$1,126
c.$1,082
d.$1,163
e.$1,008
ANS: B
Tabular solution:
FV = $1,000 (FVIF2%, 6) = $1,000 (1.1262) = $1,126.20 $1,126.
Financial calculator solution:
Inputs: N = 6; I = 2; PV =
Output: FV = $1,126.16 $1,126.
DIF: Easy 
OBJ: TYPE: Problem 
TOP: FV of a sum 
29.What is the future value of a
a15 percent interest rate?
a.$670.44
b.$842.91
c.$1,169.56
d.$1,522.64
e.$1,348.48
ANS: E
Tabular solution:
FB = $200 (FVIFA15%, 5) = $200 6.7424 = $1,348.48.
Financial calculator solution:
Inputs: N = 5; I = 15; PMT =
Output: FV = $1,348.48.
DIF: Easy 
OBJ: TYPE: Problem 
TOP: FV of an annuity 
48Chapter 4 ï The Time Value of Money
30.If a
a.$240.42
b.$263.80
c.$300.20
d.$315.38
e.$346.87
ANS: B
Tabular solution:
$1,000 = PMT (PVIFA10%, 5) PMT = $1,000/3.7908 = $263.80.
Financial calculator solution: Inputs: N = 5; I = 10; FV =
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Annuity payments 
31.You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of
a.$5,000.00
b.$6,000.00
c.$6,666.67
d.$7,500.00
e.$8,728.50
ANS: C
V = PMT/I = $1,000/0.15 = $6,666.67.
DIF: Easy 
OBJ: TYPE: Problem 
TOP: PV of a perpetuity 
32.Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?
a.$9,851
b.$13,250
c.$11,714
d.$15,129
e.$17,353
ANS: C
Chapter 4 ï The Time Value of Money 49
Tabular solution:
PV = $2,000 (PVIFA14%, 5) + $3,000 (PVIFA14%, 5) (PVIF14%, 9)
=$2,000 (3.4331) + $3,000 (2.3216) (0.5194) + $4,000 (0.3075)
=$6,866.20 + $3,617.52 + $1,230.00 = $11,713.72 $11,714.
Financial calculator solution:
Using cash flows
Inputs: C0 = 0; C1 = 2,000; Nj = 5; C2= 3,000; Nj = 3; C3 = 4,000; I = 14. Output: NPV = $11,713.54 $11,714.
DIF: Easy 
OBJ: TYPE: Problem 
TOP: PV of an uneven CF stream 
33.If $100 is placed in an account that earns a simple 4 percent, compounded quarterly, what will it be worth in 5 years?
a.$122.02
b.$105.10
c.$135.41
d.$120.90
e.$117.48
ANS: A
Tabular solution:
$100 (FVIF1%, 20) = $100 (1.2202) = $122.02.
Financial calculator solution: Inputs: N = 20; I = 1; PV =
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Quarterly compounding 
34.In 1958 the average tuition for one year at an Ivy League school was $1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the
a.12%
b.9%
c.6%
d.7%
e.8%
ANS: D
Cash flow time line:
Tabular solution:
$13,700 = $1,800 (FVIFi, 30) FVIFi, 30 = 7.6111
I ï€ 7%
50 Chapter 4 ï The Time Value of Money
Financial calculator solution:
Inputs: N = 30; PV =
Output: I = 7.0%
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Growth rate 
35.At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?
a.12 years
b.15 years
c.18 years
d.20 years
e.23 years
ANS: C
Cash flow time line:
Tabular solution:
0.5 = $1 (PVIF4%, n) PVIF4%, n = 0.5
PVIF4%, 18 = 0.4936; PVIF4%, 17 = 0.5134 n ï€ 18 years.
Although a financial calculator or interpolation might be used to solve precisely, Response c is clearly the closest and best answer of those given.
Financial calculator solution: Inputs: I = 4; PV = 1; PV =
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Effect of inflation 
36.Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks?
a.0.25%
b.0.50%
c.0.70%
d.1.00%
e.1.25%
ANS: C
Bank A: 8%, monthly
EARA =
Bank B: 9%, interest due at end of year EARB = 9%.
9.00%  8.30% = 0.70%.


Chapter 4 ï The Time Value of Money 51 
DIF: Easy 
OBJ: TYPE: Problem 
TOP: Effective annual rate 
37.Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded semiannually. If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today, what will your balance be at the end of Year 20?
a.$52,821.19
b.$57,900.83
c.$58,988.19
d.$62,527.47
e.$64,131.50
ANS: D
Cash flow time line:
Tabular solution:
Periodic
First, calculate the FV as of Year 10
FV10 yr. = ($500) (FVIFA6%, 19) 1.06 + ($500) (FVIF6%, 20)
= $500 (33.760) (1.06) + $500 (3.2071) = $19,496.35.
Calculate FV as of Year 20 using FV10 as the PV
FV20 yr. = ($19,496.35) (FVIF6%, 20) = $19,496.35 (3.2071) = $62,526.74.
Financial calculator solution:
Calculate the FV as of Year 10
BEGIN mode. Inputs: N = 20; I = 6; PMT =
Calculate the FV as of Year 20 using FV10 as the PV
END mode. Inputs: N = 20; I = 6; PMT =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: FV under semiannual compounding 
38.Assume you are to receive a
a.$6,354.81
b.$7,427.83
c.$7,922.33
d.$8,591.00
e.$6,752.46
ANS: B
52 Chapter 4 ï The Time Value of Money
Tabular solution:
FVYear 20 
= $50 (FVIFA10$, 20) = $50 (57.275) = $2,863.75. 
FVYear 30 
= $2,863 (FVIFA10$, 10) = $2,863.75 (2.5937) = $7,427.71. 
Financial calculator solution:
Calculate FV at Year 20, then take that lump sum forward 10 years to Year 30 at 10%.
Inputs: N = 20; I = 10; PMT =
At Year 30
Inputs: N = 10; I = 10; PV =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: FV of an annuity 
39.You expect to receive $1,000 at the end of each of the next 3 years. You will deposit these payments into an account which pays 10 percent compounded semiannually. What is the future value of these payments, that is, the value at the end of the third year?
a.$3,000
b.$3,310
c.$3,318
d.$3,401
e.$3,438
ANS: C
Tabular solution:
FV = $1,000(FVIF5%,4) + $1,000(FVIF5%,2) + $1,000
=$1,000(1.2155) + $1,000(1.1025) + $1,000
=$1,215.50 + $1,102.50 + $1,000 = $3,318.00.
Financial calculator solution:
Convert rSIMPLE to EAR using interest rate conversion
Inputs: P/YR = 2; NOM% =10.
Output: EFF% = EAR = 10.25%.
Solve for FV on annual basis using EAR
Inputs: N = 3; I = 10.25; PMT =
Output: FV = $3,318.006 $3,318.00.
DIF: Medium 
OBJ: TYPE: Problem 
TOP: FV of an annuity 
Chapter 4 ï The Time Value of Money 53
40.You just graduated, and you plan to work for 10 years and then to leave for the Australian "Outback" bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial "stake" be when you leave for Australia 10 years from now?
a.$21,432
b.$28,393
c.$16,651
d.$31,148
e.$20,000
ANS: D
Cash flow time line:
Tabular solution:
FV = (FVIFA8%, 10) + $1,000 (FVIFA8%, 5) + $5,000 (FVIF8%, 10)
=$1,000 (14.487) + $1,000 (5.866) + $5,000 (.1589)
=$14,487 + $5,866 + $10,794.50 = $31,147.50 $31,148
Financial calculator solution:
Solution using NFV (Note: Some calculators do not have net future value function. Cash flows can be grouped and carried forward or PV can be used; see alternative solution below.)
Inputs: 
= 5,000; 
= 1,000; Nj = 5; 
= 2,000; Nj = 5; I = 8 
Output: NFV = $31,147.79 $31,148 

Alternative solution: calculate PV of the cash flows, then bring them forward to FV using the interest rate.
Inputs: = 5,000; = 1,000; Nj = 5; = 2,000; Nj = 5; I = 8 Output: PV = $14,427.45
Inputs: N = 10; I = 8; PV =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: FV of an uneven CF stream 
41.As the winning contestant in a television game show, you are considering the prizes to be awarded. You must indicate to the sponsor which of the following two choices you prefer, assuming you want to maximize your wealth. Assume it is now January 1, and there is no danger whatever that the sponsor won't pay off.
(1)$1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying 12 percent simple annual rate, but compounded monthly (to be left on deposit for the year).
(2)$12,750 at the end of the year.
54 Chapter 4 ï The Time Value of Money
Which one would you choose?
a.Choice 1
b.Choice 2
c.Choice 1, if the payments were made at the end of the year.
d.The choice would depend on how soon you need the money.
e.Either one, since they have the same present value.
ANS: A
Tabular solution:
PVChoice 1 
= $1,000 (PVIFA 1%, 11 + 1.0) = $1,000 (11.3676) = $11,367.60 
PVChoice 2 
= $12,750 (PVIF 1%, 12) = $12,750 (0.8874) = $11,314.35 
Financial calculator solution:
Choice 1
BEGIN mode, Inputs N = 12; I = 1; PMT = 1,000.
Output: PV =
Choice 2
END mode, Inputs: N = 12; I = 1; FV  12,750.
Output: PV =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: PV of an annuity 
42.You want to buy a Nissan 350Z on your 27th birthday. You have priced these cars and found that they currently sell for $30,000. You believe that the price will increase by 5 percent per year until you are ready to buy. You can presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?
a.$4,945.57
b.$3,933.93
c.$7,714.72
d.$3,450.82
e.$6,030.43
ANS: B
Cash flow time lines:
Chapter 4 ï The Time Value of Money 55
Tabular solution:
Price of car on 27th birthday
FV = $30,000 (FVIF 5%, 7) = $30,000 (1.4071) = $42,213.
Annual investment required
FV of annuity = FVAn = PMT (FVIFA i, n)
$42,213 = PMT (FVIFA 14%, 7)
PMT = $42,213/10.7305 = $3,933.93.
Financial calculator solution:
Price of car on 27th birthday
Inputs: N = 7; I = 5; PV =
Output: FV = $42,213.01 $42,213.
Annual investment required Inputs: N = 7; I = 14; FV = 42,213. Output: PMT =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: Annuity payment 
43.Assume that your required rate of return is 12 percent and you are given the following stream of cash flows:
Year 
Cash Flow 
0$10,000
115,000
215,000
315,000
415,000
520,000
If payments are made at the end of each period, what is the present value of the cash flow stream?
a.$66,909
b.$57,323
c.$61,815
d.$52,345
e.$62,029
ANS: A
Tabular solution:
PV = $10,000 + $15,000 (PVIFA12%, 4) + $20,000 (PVIF12%, 5)
=$10,000 + $15,000 (3.0373) + $20,000 (0.5674)
=$10,000 + $45,559.50 + $11,348 = $66,907.50.
Financial calculator solution:
Using cash flows
Inputs: 
= 10,000; 
= 15,000; Nj = 4 times; 
= 20,000; I = 12. 
Output: NPV = $66,908.77 $66,909. 

Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium 
OBJ: TYPE: Problem 
TOP: PV of an uneven CF stream 
56Chapter 4 ï The Time Value of Money
44.You are given the following cash flows. What is the present value (t = 0) if the discount rate is 12 percent?
a.$3,277
b.$4,804
c.$5,302
d.$4,289
e.$2,804
ANS: A
Cash flow time line:
PV = ? 








Tabular solution: 








PV = + 
$ 1 (PVIF 12%, 1) 
= 
$ 1 (0.8929) 
= 
$ 
0.89 

+ 
$2,000 
(PVIF 12%, 2) 
= 
$2,000 
(0.7972) 
= 
$ 
1,594.40 
+ 
$2,000 
(PVIF 12%, 3) 
= 
$2,000 
(0.7118) 
= 
$ 
1,423.60 
+ 
$2,000 
(PVIF 12%, 4) 
= 
$2,000 
(0.6355) 
= 
1,271.00 

+ 
(PVIF 12%, 6) 
= 
(0.5066) 
= 
1,013.20 


PV 
= 
$3,276.69 
Financial calculator solution: 




Inputs: 




Output: NPV = $3,276.615 $3,277 




DIF: Medium 
OBJ: TYPE: Problem 
TOP: 
PV of an uneven CF stream 
45.You are given the following cash flow information. The appropriate discount rate is 12 percent for Years
Year 
Amount 
$20,000 

$25,000 
What should you be willing to pay right now to receive the income stream above?
a.$166,866
b.$158,791
c.$225,000
d.$125,870
e.$198,433
ANS: D
Tabular solution:
Chapter 4 ï The Time Value of Money 57
Years
PV of annuity Years
Years
PV5 = $25,000 (PVIFA10%, 5) = $25,000 (3.7908) = $94,770
PV of annuity Years
PV0 = $94,770 (PVIF 12%, 5) = $94,770 (0.5674) = $53,772.50
PV0 of both annuities
$72,096 + $53, 772.50 = $125.868.50 $125.870
Financial calculator solution:
Solve for PV at time = 0 of $20,000 annuity
Inputs:
Solve for PV at time = 5 pf $25,000 annuity using its value at t = 5
Inputs:
Solve for PV at time = 0 0f $25,000 annuity
Inputs: N = 5; I = 12; FV =
Add the two PVs together
PVBoth annuities = $72,095.524 + $53,774.855 = $125,870.38 $125.870
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium 
OBJ: TYPE: Problem 
TOP: PV of an uneven CF stream 
46.A project with a

Year 1 

Year 2 

Year 3 
Prob 
Cash Flow 
Prob 
Cash Flow 
Prob 
Cash Flow 
0.30 
$300 
0.15 
$100 
0.25 
$200 
0.40 
500 
0.35 
200 
0.75 
800 
0.30 
700 
0.35 
600 




0.15 
900 


Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.)
a.$1,204.95
b.$835.42
c.$1,519.21
d.$1,580.00
e.$1,347.61
ANS: E
Calculate expected cash flows 





E(CF1) 
= (0.30) ($300) + (0.40) 
($500) 
+ (0.30) 
($700) 
= $500 
E(CF2) 
= (0.15) ($100) + (0.35) 
($200) 
+ (0.35) 
($600) 
+ (0.15) ($900) = $430 
E(CF3) 
= (0.25) ($200) + (0.75) 
($800) 
= $650 


58 Chapter 4 ï The Time Value of Money
Tabular solution:
PV = $500 (PVIF 8%, 1) + $430 (PVIF 8%, 2) + $650 (PVIF 8%, 3)
=$500 (0.9259) + $430 (0.8573) + $650 (0.7938)
=$462.95 + $368.64 + $515.97 = $1,347.56
Financial Calculator Solution:
Using cash flows,
Inputs:
Output: NPV = $1,347.61
DIF: Medium 
OBJ: TYPE: Problem 
TOP: PV of uncertain cash flows 
47.If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?
a.$20,593
b.$31,036
c.$24,829
d.$50,212
e.$6,667
ANS: C
Tabular solution: 



Initial balance 
= 0.8($250,000) = $200,000 


$200,000 
= PMT (PVIA12%, 30) 


$200,000 
= PMT (8.0552) 


PMT 
= $200,00/8.0552 = $24,828.68 $24,829 

Financial calculator solution: 


Inputs: N = 30; I = 12; PV = 


Output: PMT = $24,828.73 
$24,829 


DIF: Medium 
OBJ: 
TYPE: Problem 
TOP: Amortization 
48.In its first year of operations, 1999, the Gourmet Cheese Shoppe had earnings per share (EPS) of $0.26. Four years later, in 2003, EPS was up to $0.38, and 7 years after that, in 2010, EPS was up to $0.535. It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained. What are the rates of growth for the earlier period and for the later period?
a.6%; 5%
b.6%; 3%
c.10%; 8%
d.10%; 5%
e.12%; 7%
ANS: D
Chapter 4 ï The Time Value of Money 59
Tabular solution:
PV = $0.26 = $0.38 (PVIFi, 4) PVIF i, 4 = $0.26/$0.38 = 0.6842
i1 ï€ 10%
PV = $0.38 = $0.535 (PVIF i, 7) PFIV i,7 = $0.38/$0.535 = 0.7103
i2 ï€ 5%
Financial calculator solution:
Inputs: N = 4; PV =
DIF: Medium 
OBJ: TYPE: Problem 
TOP: Growth rate 
49.Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000 on a loan which requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding
a.0.31%
b.0.53%
c.0.75%
d.0.96%
e.1.25%
ANS: D
EARQuarterly =
EARDaily =
Difference = 10.38%  9.42% = 0.96%
Alternatively, with a financial calculator, for the quarterly loan enter P/YR = 4, NOM% = 10, and press EFF% to get EAR = 10.38%.
For the daily loan, enter P/YR = 365, NOM = 9%, and press EFF% to get EAR = 9.42%.
DIF: Medium 
OBJ: TYPE: Problem 
TOP: Effective annual rate 
50.You are currently at time period 0, and you will receive the first payment on an annual payment annuity of $100 in perpetuity at the end of this year. Six full years from now you will receive the first payment on an additional $150 in perpetuity, and at the end of time period 10 you will
60 Chapter 4 ï The Time Value of Money
receive the first payment on an additional $200 in perpetuity. If you require a 10 percent rate of return, what is the combined present value of these three perpetuities?
a.$2,349.50
b.$2,526.85
c.$2,685.42
d.$2,779.58
e.$2,975.40
ANS: D
Tabular solution:
PV = ($100/0.10) + ($150/0.10)(PVIF 10%, 5) + ($200/0.10)(PVIF 10%, 9)
=$1,000 + $1,500 (0.6209) + $2,000 (0.4241)
=$1,000 + $931.35 + $848.20 = $2,779.55
Financial calculator solution:
Calculate the undiscounted values of each of three perpetuities at the point in time where they begin, using numerical methods, then calculate PV at t = 0 of the combined perpetuity values.
PVp1 at Time = 0: $100/0.10 = $1,000
PVp2 at Time = 5; $150/0.10 = $1,500
PVp3 at Time = 9; $200/0.10 = $2,000
Inputs: Output: NPV = $2,446.577 $2,779.58.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Tough 
OBJ: TYPE: Problem 
TOP: PV of a perpetuity 
51.Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow of $200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at
a.$528.21
b.$1,329.00
c.$792.49
d.$1,046.41
e.$875.18
ANS: C
Chapter 4 ï The Time Value of Money 61
Tabular solution:
PV =
=
=
Financial calculator solution:
Inputs:
Output: NPV =
Calculate the PV of CFs
Inputs:
Output:
Calculate PV of the FV of the positive CFs at Time = 3
Inputs: N = 3; I = 4; FV =
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Tough 
OBJ: TYPE: Problem 
TOP: PV of an uneven CF stream 
52.Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years. Right now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this cost to rise by 8 percent per year in all future years.
You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the future. You want to maintain the same standard of living while in law school that $17,000 per year would currently provide. You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns. How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of
aconstant amount.)
a.$13,242.67
b.$6,562.13
c.$10,440.00
d.$7,153.56
e.$14,922.85
ANS: D
62 Chapter 4 ï The Time Value of Money
PVCosts = $17,000, I = 8%
PVAcct = $25,000, I = 9.31% Financial calculator solution:
Step 1: Use the current law school costs and inflation rate to calculate the withdrawals to cover law school costs at T = 4, 5, 6:
At T = 4, Inputs: N = 4, PV =
Step 2: Use interest rate conversion feature to calculate the effective annual rate of the 9% account, compounded quarterly.
Inputs: NOM% = 9; P/YR = 4. Output: EFF% = 9.31%
Step 3: Use the EAR from Step 2 to determine the PV of law school payments at T = 4, 5, 6 as of T = 4.
Inputs: Output: NPV = $68,556.73 which equals PVT=4, costs
Step 4: Determine the VF at T = 4 of the $25,000 in the account as of T = 0:
Inputs: N = 4; I = 9.31; PV =
Step 5: Calculate shortfall between what the account needs to have and will actually have at T = 4:
$68,556.73  $35,692.72 = $32,864.01
Step 6: Calculate the annuity payments, which will earn 9.31% EAR and accumulate to an FV of $32,864.01 at T = 4:
Inputs: N = 4; I = 9.31%; FV = 32,864.01. Output: PMT = $7,153.56
DIF: Tough 
OBJ: TYPE: Problem 
TOP: Annuity payments 
Chapter 4 ï The Time Value of Money 63
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
53.You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend's proposal than under your proposal?
a.0.00%
b.0.45%
c.0.68%
d.0.89%
e.1.00%
ANS: C Your proposal:
EAR1 = $120/$1,000 EAR1 = 12%
Your friend's proposal:
Interest is being paid each month ($10/$1,000 = 1% per month), so it compounds, and the EAR is higher than rsimple = 12%:
EAR2 = Difference = 12.68%
You could also visualize your friend's proposal in a cash flow time line format:
Insert those cash flows in the cash flow register of a calculator and solve for IRR. The answer is 1%, but this is a monthly rate. The simple rate is 12 (1%) = 12%, which converts to an ER of 12.68% as follows:
Input into a financial calculator the following:
P/YR = 12, NOM% = 12, and solve for EFF% = 12.68%
DIF: Easy 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
54.Suppose you put $100 into a savings account today, the account pays a simple annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made?
a.$226.20
b.$115.35
c.$62.91
d.$9.50
e.$3.00
ANS: D
64 Chapter 4 ï The Time Value of Money
Tabular/Numerical solution:
Solve for amount on deposit at the end of 6 months.
Step 1: FV = $100 (FVIF 3%, 1)  $100 = $3.00
FV = $100 (1 + 0.06/2)  $100 = $3.00
Step 2: Compound the $3.00 for 39 periods at 3%
FV = $3.00 (FVIF 3%, 39) = $9.50
Since table does not show 39 periods, use numerical/calculator exponent method. FV = $3.00 (1 + 0.06/2)39 = $9.50
Financial calculator solution: (Step 2 only) Inputs: N = 39; I = 3; PV =
Output: FV = $9.50
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: FV of a sum 
55.A bank pays a quoted annual (simple) interest rate of 8 percent. However, it pays interest (compounds) daily using a
a.7.86%
b.7.54%
c.8.57%
d.8.33%
e.9.21%
ANS: D
Numerical solution:
EAR =
Effective rate 8.33%
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 365; NOM% = 8.
Output: EFF% = EAR = 8.328% 8.33%
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
56.You can deposit your savings at the Darlington National Bank, which offers to pay 12.6 percent interest compounded monthly, or at the Bartlett Bank, which will pay interest of 11.5 percent compounded daily. (Assume 365 days in a year.) Which bank offers the higher effective annual rate?
a.Darlington National Bank.
b.Bartlett Bank.
c.Both banks offer the same effective rate.
d.Cannot be determined from the information provided.
e.Workable only if the banks use the same compounding period.
ANS: A
Chapter 4 ï The Time Value of Money 65
Numerical solution:
Darlington
EAR =
Bartlett
EAR =
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 12; NOM% = 12.6. Output: EFF% = EAR = EARDarlington = 13.354% Inputs: P/YR = 365; NOM% = 11.5. Output: EFF% = EARBartlett = 12.185%.
EARDarlington > EARBartlett
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
57.You have just taken out a
a.15.87%
b.14.75%
c.13.38%
d.16.25%
e.16.49%
ANS: A
Financial calculator solution:
Calculate periodic rate
Inputs: N = 3600; PV =
Output: I = 1.235% per period.
Use interest conversion feature
Inputs: NOM% = 1.235% 12 = 14.82; P/YR = 12
Output: EFF% = 15.868% 15.87%
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
58.You have just borrowed $20,000 to buy a new car. The loan agreement calls for 60 monthly payments of $444.89 each to begin one month from today. If the interest is compounded monthly, then what is the effective annual rate on this loan?
a.12.68%
b.14.12%
c.12.00%
d.13.25%
e.15.08%
ANS: A
66 Chapter 4 ï The Time Value of Money
Tabular solution:
$20,000 = $444.89 (PVIFA r, 60) PVIFA r, 60 = 44.9549
r = 1%
EAR
Financial calculator solution:
Calculate periodic rate and simple rate
Inputs: N = 60; PV =
Output: I = 1.0. NOM% = 1.0% 12 = 12.00%
Use interest rate conversion feature
Inputs: P/YR = 12; NOM% = 12.0.
Output: EFF% = EAR = 12.68%
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
59.Bank A offers a
a.9.67%
b.9.76%
c.9.83%
d.9.87%
e.9.93%
ANS: B
Numerical solution:
1.10= (1 + r/2)2
1.0488 
= 1 + r/2 
r/2 
= 0.0488 
r 
= 0.0976 = 9.76% 
Financial calculator solution:
Use interest rate conversion feature
Inputs: P/YR = 2; EFF% = 10.0%.
Output: NOM% = 9.462% 9.76%

Chapter 4 ï The Time Value of Money 67 
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Effective interest rates 
60.Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8 percent simple (quoted) interest rate, but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?
a.$1,000
b.$866
c.$1,050
d.$901
e.$893
ANS: E
Financial calculator solution:
Calculate the EAR on the bank deposit
Inputs: P/YR = 4, NOM% = 8; Output: EFF% = EAR = 8.24%
Calculate the PV of the investment
Inputs: N = 4; I = 8.24; PMT = 50; FV = 1,000
Output: PV =
Alternate method: Using cash flows
Inputs:
Output: NPV = $893.26 $893
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: PV and effective annual rate 
61.Your company is planning to borrow $1,000,000 on a
a.29.83%
b.57.18%
c.35.02%
d.64.45%
e.72.36%
ANS: B Tabular solution:
$1,000,000 = PMT(PVIFA15%,5)
PMT = $1,000,000/3.3522 = $298,311.56.
Construct amortization table
Year 
Beg Balance 
Payment 
Interest 
Principal 
End Balance 
68 Chapter 4 ï The Time Value of Money
1 
$1,000,000 
$298,312 
$150,000 
$148,312 
$851,688 
2 
851,688 
298,312 
127,753 
170,559 
681,129 
Principal fraction of PMT = $170,559/$298,312 = 0.57175 Ã· 57.18%.
Financial calculator solution:
Calculate the principal portion of PMT using amortization function: (Note: The steps below are specific to the
Inputs: N = 5; I = 15; PV =
Output: = or PRIN = 170,562.89.
Principal fraction = $170,562.89/$298,315.55 = 0.57175 57.18%.
Note: Difference in amortization payment and principal calculation due to rounding. Answer is unaffected.
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Amortization 
62.The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8 percent, quarterly compounding. The loan is to be amortized in
a.$15,675.19
b.$18,508.81
c.$21,205.33
d.$24,678.89
e.$28,111.66
ANS: B
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Amortization 
Chapter 4 ï The Time Value of Money 69
63.You have a
a.1.50%
b.3.42%
c.5.23%
d.6.75%
e.8.94%
ANS: E
Enter the information into the calculator to use its amortization feature:
N 
= 360 
I/YR 
= 8.5/12 = 0.7063 
PMT 
= 1,000 
FV 
= 0 
Solve for PV =
Enter: 1 INPUT 36 AMORT
Int 1  36 = $32,782.14
Prin 1  36 = $3,217.86
Total payments 1  36 = $36,000.
Percentage of total payments which is principal =
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: Amortization 
64.Your company must make payments of $100,000 each year for 10 years, with the first payment to be made 10 years from today. To prepare for these payments, your company must make 10 equal annual deposits into an account which pays a simple interest rate of 7 percent, daily compounding
a.$47,821.11
b.$49,661.86
c.$51,234.67
d.$52,497.33
e.$53,262.39
ANS: B
The FV of the DEP annuity at T = 10 must be sufficient to make the 10 payments of $100,000 each.
Step 1: Find the PV of the $100,00 payments at the end of Year 10. This is a
70 Chapter 4 ï The Time Value of Money
Use the interest conversion feature on your financial calculator to find EAR = 7.2501%
P/YR = 360
NOM% = 7
Solve for EFF% = 7.2501%
Now find the PV of the annuity:
Step 2: Determine the amount of the annuity due by using the present value of the $100,000 payments at Year 10 as the future value of the annuity due.
Deposits of $49.661.86 will provide the needed funds.
DIF: 
Medium 
OBJ: TYPE: Financial Calculator 
TOP: 
Annuities and daily compounding 
65.Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new
a.
b.
c.+$125.30
d.+$253.62
e.+$509.81
ANS: B
Chapter 4 ï The Time Value of Money 71
Solve for NPV =
Therefore, the PV of payments under the proposed lease would be greater than the PV of payments under the old lease by $6,094.23  $5,840.61 = $253.62. Thus, your net worth would decrease by $253.62.
DIF: 
Medium 
OBJ: TYPE: Financial Calculator 
TOP: 
NPV and 
66.You plan to invest $2,500 in a money market account which will pay an annual stated (simple) interest rate of 8.75 percent, but which compounds interest on a weekly basis. If you leave this money on deposit for one year (52 weeks), what will be your ending balance when you close the account?
a.$2,583.28
b.$2,611.72
c.$2,681.00
d.$2,703.46
e.$2,728.50
ANS: E
Numerical solution:
FV =
Financial calculator solution:
Convert simple rate to EAR
Inputs: P/YR = 52; NOM% = 8.75.
Output: EFF% = EAR + 9.1362% 9.14%
Calculate FV
Inputs: N = 1; I = 9.14; PV =
Output: FV = $2,728.50
DIF: Medium 
OBJ: TYPE: Financial Calculator TOP: 
67.You have just purchased a life insurance policy that requires you to make 40 semiannual payments of $350 each, where the first payment is due in 6 months. The insurance company has guaranteed that these payments will be invested to earn you an effective annual rate of 8.16 percent, although interest is to be compounded semiannually. At the end of 20 years (40 payments), the policy will mature. The insurance company will pay out the proceeds of this policy to you in 10 equal annual payments, with the first payment to be made one year after the policy matures. If the effective interest rate remains at 8.16 percent, how much will you receive during each of the 10 years?
a.$6,113.20
b.$5,244.62
c.$5,792.21
d.$4,992.39
e.$4,723.81
72 Chapter 4 ï The Time Value of Money
ANS: D
Tabular solution: (Part a)
Value of the policy at the end of 20 years
FV = $350 (FVIFA 4%, 40) = $350 (95.026) = $33,259.10 This amount is then to be paid out over a
Note: There is no tabular solution presented for part b due to fractional interest rate (EAR = 8.16%)
Financial calculator solution: (Part a)
Inputs: N = 40; I = 4; PMT =
Financial calculator solution (Part b)
Inputs: N = 10; I = 8.16; PV = 33,258.93.
Output: PMT = $4,992.39.
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
68.Assume that you just had a child, and you are now planning for her college education. You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at
a.$705.86
b.$731.93
c.$692.15
d.$650.46
e.$785.72
ANS: B
Chapter 4 ï The Time Value of Money 73
Financial calculator solution:
Calculate college cost at 8% growth for 5 years
Inputs: N = 5; I = 8; PV =
Output: FV5 = $8.815.97
Calculate FV of tuition cost in Years 18 through 21 at 5% growth
Inputs: N = 13; I = 5; PV = 
FV18 
= $16,623.83 
N = 14 
FV19 
= $17,455.02 
N = 15 
FV20 
= $18.327.77 
N = 16 
FV21 
= $19,244.16 
Use cash flows to discount FVs to PV
Inputs:
Output: NPV = $15,506.49
Calculate payment based on PV of costs
BEGIN mode Inputs: N = 43; I = 4; PV =
Output: PMT = $731.93
Alternate solution for payment using END mode and FV of costs:
Use cash flows to compound costs to NPV:
Inputs:
Output: NFV = $80,521.83
END mode:
Inputs: N = 43; I = 4; PV = 0; FV = 80,521.83
Output: MPT =
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
69.Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. He wants a retirement income which has, in the first year, the same purchasing power as $40,000 has today. However, his retirement income will be of a fixed amount, so his real income will decline over time. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a.$1,863
b.$2,034
c.$2,716
d.$5,350
e.$6,102
ANS: C
74 Chapter 4 ï The Time Value of Money
Step 1: The retirement payments, which begin at t = 2, must be: $40,000 (1 + Infl)2 = $40,000 (1.05)2 = $44,100
Step 2: There will be 3 retirement payments of $44,100, made at t = 2, t = 3, and t = 4. We find the PV of an annuity due at t = 2 as follows:
Set calculator to "Begin". Then enter:
N = 3; I = 8, PMT = 44,100; FV = 0. Solve for PV = $122,742.
If he has this amount at t = 2, he can receive the 3 retirement payments.
Step 3: The $100,000 now on hand will compound at 8% for 2 years: $100,000 (1.08)2 = $116,640
Step 4: So, he must save enough each year to accumulate an additional $122,742  $116,640
 $6,102: 

Need at t = 2 
$122,742 
Will have 
(116,640) 
Net additional needed 
$ 6,102 
Step 5: He must make 2 payments, at t = 0 and at t = 1, such that they will grow to a total of $6,102 at t = 2
This is the FV of an annuity due found as follows: Set calculator to "Begin". Then enter:
N = 2; I = 8; PV = 0; FV = 6,102. Solve for PMT = $2,716
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
70.Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. Suppose your father wants to have a real income of $40,000 in today's dollars in each year after he retires. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a.$1,863
b.$2,034
c.$2,716
d.$5,350
e.$6,102
ANS: D
Chapter 4 ï The Time Value of Money 75
Step 1: The retirement payments, which begin at t = 2, must be: t = 2: $40,000 (1.05)2 = $44,100
t = 3: $44,100 (1.05) = $46,305 t = 4: $46, 305 (1.05) = $48.620
Step 2: Now we need enough at t = 2 to make the 3 retirement payments as calculated in Step 1. We cannot use the annuity method, but we can enter, in the cash flow register, the following:
Then enter I = 8, and press NPV to find NPV = PV = $128,659
Step 3: The $100,000 now on hand will compound at 8% for 2 years: $100,000 (1.08)2 = $116,640.
Step 4: The net funds needed are:
Need at t = 2 
$128,659 
Will have 
(116,640) 
Net needed 
$ 12,019 
Step 5: Find the payments needed to accumulate $12,019. Set the calculator to "Begin" and then enter:
N = 2; I = 8; PV = 0; FV = 12,019. Solve for PMT = $5,350.
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
71.Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw $50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw $73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave $200,000 to her descendants. Your client currently has $100,000. You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years. Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday). How much should she contribute each year in order to meet her objectives?
76Chapter 4 ï The Time Value of Money
a.$12,401.59
b.$12,998.63
c.$13,243.18
d.$13,759.44
e.$14,021.53
ANS: A
Value of cash outflows:
Age 85 
= ($ 50,000) 

= ( 55,000) =
= ( 60,000) =
= ( 66,550) =
= ( 73,205) =
= ( 200,000)
Solve for NPV at 8% = ($395, 548.96). Value for $100,000 at age 85; $100,000 (1.08)10 = $215,892.50
Shortfall at age 85 = $215,892.50  $395,548.96 = ($179,656.46).
Calculate annual payments to equal this shortfall: N = 10; I/YR = 8; PV = 0; FV = 179,656.46. Solve for PMT = $12,401.59
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
72.You are considering an investment in a
a.$35
b.$38
c.$40
d.$45
e.$50
ANS: C
Chapter 4 ï The Time Value of Money 77
Calculate the NPV of payments in Years
= 30 I = 8
Solve for NPV = $298.25
Difference between the security's price and PV of payments: $360.36  $298.25 = $62.14
Calculate the FV of the difference between the purchase price and PV of payments, Year 1  23: N = 23
I = 8
PV =
Solve for FV = $364.85.
Calculate the value of the annuity payments in Years
I = 8
PV =
Solve for PMT = $40
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
73.You are currently saving for your child's college education. The current cost of college is $10,000
ayear. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a
a.$1,133.16
b.$1,393.42
c.$1,477.02
d.$1,507.81
e.$1,622.33
ANS: B
78 Chapter 4 ï The Time Value of Money
Step 1: Calculate college costs at t = 10, 11, 12, 13: t = 10; (10,000) (1.05)10 = $16,288.95
t = 11: (10,000) (1.05)11 = $17,103.39 t = 12: (10,000) (1.05)12 = $17,958.56 t = 13: (10,000) (1.05)13 = $18,856.49
Step 2: Find the NPV of the cash flows:

= 
25,000 

= 
0 

= 
16,288.95 

= 


= 


= 

I 
= 
6 
Solve for NPV =
Step 3: Find the payment stream which equates to the NPV.
BEGIN
N = 10
I = 6
PV =
FV = 0
Solve for PMT = $1,393.42
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Annuity payments 
74.You will receive a $100 annual perpetuity, the first payment to be received now, at Year 0, a $300 annual perpetuity payable starting at the end of Year 5, and a $200 semiannual (2 payments per year) perpetuity payable starting midway through Year 10. If you require an effective annual interest rate of 14.49 percent, what is the present value of all three perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)
a.$2,091.86
b.$2,785.14
c.$4,213.51
d.Infinite; the present value of any perpetuity is infinite.
e.Cannot determine the value since some payments are annually and some semiannually.
ANS: B
Numerical solution:
PV = $100 + ($100/0.1449)+ ($300/0.1449) [1/(1.1449)4] + ($200/0.1449) [1/(1.449)9]
+($200/0.1449) [1/(1.1449)9.5]
=$100 + $690.13 + $1,204.99 + $408.37 + $318.65 = $2785.14
Financial calculator solution:
Step 1: Calculate the values of the respective perpetuities as their starting points; t =
semiannual periods. 

PVp1 = 100 + 100/0.1449 = 790.13 
n = 0 


Chapter 4 ï The Time Value of Money 79 

FVp2, t = 8 = 300/0.1449 = 2,070.3 
n = 8 semiannual periods 


1/2FVp3, t = 18 = 200/0.1449 = 1,380.26 
n = 18 semiannual periods 


1/2FVp3, t = 19 = 200/0.1449 = 1,380.26 
n = 19 semiannual periods 


Step 2: Use interest at conversion to convert EAR to NOM% 




Inputs: P/YR = 2; EFF% = EAR = 14.49. Output: NOM% = 14.0% 



Periodic rate = 14/2 = 7.0% 





Inputs: 
N = 8; I = 7; FV = 
Output 
PV 
= 
$1,204.99 

N = 18; I = 7; FV = 

PV 
= 
408.37 

N = 19; I = 7; FV = 

PV 
= 
381.65 

Plus PV of perpetuity one 

PV 
= 
790.13 





$2,785.14 
PV of all perpetuities = $2,785.14 





DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: 
PV of an annuity 
75.Hillary is trying to determine the cost of health care to college students, and parents' ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children's costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings can be invested at a simple rate of 6 percent, annual compounding. Hillary wants a health care plan which covers the fully inflated cost of health care for a student for 4 years, during years 19 through 22 (with payments made at the end of years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent's share of a child's college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding.
a.$1,082.76
b.$3,997.81
c.$5,674.23
d.$7,472.08
e.$8,554.84
ANS: D 


Parent's savings: 
Health Care Costs, Years 

N = 18 
= 

I = 8 
$1,000 (1.1)20 
= 
PMT = 100 
$1,000 (1.1)21 
= 
FV = 0 
= 

Solve for PV = $1,082.76 


= 0 = 0
80 Chapter 4 ï The Time Value of Money

= 


= 


= 


= 

I 
= 
6 
Solve for NPV =
Consequently, the government must set aside $8,554.84  $1,082.76 = $7,472.08 Alternatively,
= 0
= 100
=
=
=
=
Solve for NPV =
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: PV of an uneven CF stream 
76.You have some money on deposit in a bank account which pays a simple (or quoted) rate of 8.0944 percent, but with interest compounded daily (using a
a.1.87%
b.1.53%
c.2.00%
d.0.96%
e.0.44%
ANS: C
Numerical solution:
Step 1: Find the effective annual rate (EAR) of interest on the bank deposit
EARDaily = (1 + 0.080944/365)365
$8,000 = $10,000/(1 + r)2.25 (1 + r)2.25 = 1.25
1 + r = 1.25(1/2.25)
1 + r = 1.10426
r = 0.10426 ï€ 10.43%
Step 3: Difference = 10.43%  8.43% = 2.0%
Financial calculator solution:
Chapter 4 ï The Time Value of Money 81
Calculate EARDaily using interest rate conversion feature
Inputs: P/YR = 365; NOM% = 8.0944; Output: EFF% = EAR = 8.43%
Calculate EAR of the equal risk investment
Inputs: N = 2.25; PV =
Difference: 10.43%  8.43% = 2.0%
DIF: Tough 
OBJ: TYPE: Financial Calculator TOP: Effective annual rate 
77.Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early retirement. The first payment will be made 3 months from now. At the end of 20 years (80 payments), you will be paid 10 equal annual payments, with the first payment to be made at the beginning of Year 21 (or the end of Year 20). The funds will be invested at a simple rate of 8.0 percent, quarterly compounding, during both the accumulation and the distribution periods. How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.)
a.$7,561
b.$10,789
c.$11,678
d.$12,342
e.$13,119
ANS: B
PMT = ?
Find the FV at t = 80 of $400 quarterly payments: N = 80; I = 2; PV = 0; and PMT = 400.
Solve for FV = $77,508.78
Find the EAR of 8%, compounded quarterly, so you can determine the value of each of the receipts.
EAR =
Now, determine the value of the receipts, remembering that this is an annuity due. With a financial calculator, input the following:
N = 10; I = 8.2432; PV =
DIF: 
Tough 
OBJ: TYPE: Financial Calculator 
TOP: 
PMT and quarterly compounding 