Time Value of Money

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Chapter 5: Time Value of Money

Multiple Choice Questions
1. What is the total amount accumulated after three years if someone invests $1,000 today with a simple annual interest rate of 5 percent? With a compound annual interest rate of 5 percent? A. $1,150, $1,103

B. $1,110, $1,158
C. $1,150, $1,158
D. $1,110, $1,103
Level of difficulty: Easy
Solution: C.
Simple interest rate: $1,000 + ($1,000)(5%)(3) = $1,150
Compound interest rate: $1,000(1.05)3 = $1,158

2. Which of the following has the largest future value if $1,000 is invested today? A. Five years with a simple annual interest rate of 10 percent B. 10 years with a simple annual interest rate of 8 percent C. Eight years with a compound annual interest rate of 8 percent D. Eight years with a compound annual interest rate of 7 percent Level of difficulty: Easy

Solution: C.
A) $1,000 + ($1,000)(10%)(5) = $1,500
B) $1,000 + ($1,000)(8%)(10) = $1,800
C) $1,000(1.08)8 = $1,851
D) $1,000(1.07)8 = $1,718
Therefore, C is the largest.

Interest rates in the following questions are compound rates unless otherwise stated

3. Suppose an investor wants to have $10 million to retire 45 years from now. How much would she have to invest today with an annual rate of return equal to 15 percent? A. $18,561
B. $17,844
C. $20,003
D. $21,345
Level of difficulty: Medium
Solution: A.
PV=$10,000,000/(1.15)45=10,000,000/538.7693=$18,561
Or using a financial calculator (TI BAII Plus),
N=45, I/Y=15, PMT=0, FV=10,000,000, CPT PV= –18,561

4. Which of the following is false?
A. The longer the time period, the smaller the present value, given a $100 future value and holding the interest rate constant. B. The greater the interest rate, the greater the present value, given a $100 future value and holding the time period constant. C. A future dollar is always less valuable than a dollar today if interest rates are positive. D. The discount factor is the reciprocal of the compound factor. Level of difficulty: Medium

Solution: B. The greater the interest rate, the smaller the present value, given a $100 future value and holding time period constant.

5. Maggie deposits $10,000 today and is promised a return of $17,000 in eight years. What is the implied annual rate of return? A. 6.86 percent
B. 7.06 percent
C. 5.99 percent
D. 6.07 percent
Level of difficulty: Medium
Solution: A.
FV=PV(1+k)n
17,000=10,000(1+ k)8
8ln(1+k)=ln(1.7), therefore k=6.86%
Or using a financial calculator (TI BAII Plus),
N=8, PV= –10,000, PMT=0, FV=17,000, CPT I/Y=6.86%

6. To triple $1 million, Mika invested today at an annual rate of return of 9 percent. How long will it take Mika to achieve his goal? A. 15.5 years
B. 13.9 years
C. 12.7 years
D. 10 years
Level of difficulty: Medium
Solution : C.
FV=PV(1+k)n
(3)(1,000,000)=1,000,000(1.09) n
ln(3)=(n)ln(1.09)
n=12.7 years
Or using a financial calculator (TI BAII Plus),
I/Y=9, PV= –1,000,000, PMT=0, FV=3,000,000, CPT N=12.7

7. Which of the following concepts is incorrect?
A. An ordinary annuity has payments at the end of each year. B. An annuity due has payments at the beginning of each year. C. A perpetuity is considered a perpetual annuity.
D. An ordinary annuity has a greater PV than an annuity due, if they both have the same periodic payments, discount rate and time period. Level of difficulty: Medium
Solution: D. The annuity due has a greater PV because it pays one year earlier than ordinary annuity.

8. Jan plans to invest an equal amount of $2,000 in an equity fund every year-end beginning this year. The expected annual return on the fund is 15 percent. She plans to invest for 20 years. How much could she expect to have at the end of 20 years? A. $237,620

B. $176,424
C. $204,887
D. $178,424
Level of...
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