1 Which of the following statements is true of time value of

1. Which of the following statements is true of time value of money? A) A dollar received today is worth more than a dollar to be received in the future because future dollars are not affected by inflation. B) A dollar received today is worth less than a dollar to be received in the future because future dollars are not affected by inflation. C) A dollar received today is worth more than a dollar to be received in the future because funds received today can be invested to earn a return. D) A dollar to be received in the future is worth more than a dollar received today because it would have less risk associated with it.

2. Future value measures: A) what one or more cash flows are worth at the end of a specified period. B) what one or more cash flows that is to be received in the future will be worth today. C) the value of an investment after subtracting interest earned on it for one or more periods. D) the value of an investment’s worth today.

3. The process of converting an amount given at the present time into a future value is called: A) annualizing. B) discounting. C) compounding. D) capital budgeting.

4. Which of the following is true of the future value of an investment? A) The higher the interest rate, the higher the future value of an investment B) The higher the inflation rate, the lower the future value of an investment. C) The lower the number of compounding periods, the higher the future value of an investment. D) The lower the present value of an investment, the higher the future value of an investment.

5. Joseph Ray just received an inheritance of $35,775 from his great aunt. He plans to invest the funds for retirement. If Joseph can earn 4.75% per year with quarterly compounding for 32 years, how much will he have accumulated? (Round off to the nearest dollar.) A) $237,416 B) $71,550 C) $184,622 D) $162,113

6. Lori Willis plans to invest for retirement, which she hopes will be in 20 years. She is planning to invest $25,000 today in U.S. Treasury bonds that will earn interest at 6.25 percent annually. How much will she have at the end of 20 years? (Round to the nearest dollar.) A) $68,870 B) $50,625 C) $84,046 D) $75,000

7. Dynoxo Textiles has a cash inflow of $1 million, which it needs for a long-term investment, at the end of one year. It plans to deposit the money in a bank CD that pays daily interest at 4.50 percent. What will be the value of the investment at the end of the year? (Round to the nearest dollar.) A) $1,020,475 B) $1,000,103 C) $1,037,500 D) $1,046,025

8. Your mother is trying to choose one of the following bank CDs to deposit $10,000. Which will have the highest future value if she plans to invest for three years? A) 3.50% compounded daily B) 3.25% compounded monthly C) 3.40% compounded quarterly D) 3.75% compounded annually

9. Jack Palomo has deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? If the account paid compound interest, what would be the interest on interest in five years? A) $750; $95.56 B) $150; $845.56 C) $150; $95.56 D) $95.56; $845.56

10. Richard McLean wants to invest $3,000 in an account paying 5.25 percent compounded quarterly. What is the interest on interest after four years? A) $695.98 B) $65.98 C) $630.00 D) $157.50

11. Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest on interest after six years? A) $8,662.50 B) $10,925.44 C) $2,497.63 D) $1,092.48

12. Joseph Harris is considering an investment that pays 6.5 percent annually. How much must he invest today such that he will have $25,000 in seven years? (Round to the nearest dollar.) A) $17,474 B) $18,850 C) $16,625 D) $16,088

13. When discount rate: A) increases, the present value of a future cash flow decreases. B) increases, the present value of a future cash flow increases. C) decreases, the present value of a future cash flow will remain the same. D) decreases, the present value of a future cash flow decreases.

14. Leroy Diaz plans to invest some money today so that he will receive $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today? A) $5,276 B) $6,722 C) $6,897 D) $7,140

15. You need to have $15,000 in five years to payoff a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.) A) $4,903 B) $11,275 C) $13,184 D) $12,250

16. Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.) A) $6,432 B) $7,826 C) $8,148 D) $7,763

17. The process of converting future cash flows to what its present value is called: A) annualizing. B) discounting. C) compounding. D) capital budgeting.

18. Anne Morgan wants to borrow $6,000 for a period of four years. She has two choices. Her bank is offering to lend her the amount at 7.25 percent compounded annually. She can also borrow from her firm and will have to repay a total of $8,130.93 at the end of four years. Should Anne go with her bank or the firm, and what is the interest rate if she borrows from her firm? (Round to the nearest percent.) A) She should borrow from the bank as the bank is charging a higher interest of 9%. B) She should borrow from her firm as it is charging a lower interest of 7%. C) She should borrow from the bank as the firm is charging a higher interest of 8%. D) She should borrow from her firm as it is charging a lower interest of 6%.

19. Patrick Smith has $5,000 to invest in a small business venture. His partner has promised to pay him back $8,200 in five years. What is the return earned on this investment? A) 9.3% B) 8.7% C) 11.1% D) 10.4%

Solution

1.

Answer is C) A dollar received today is worth more than a dollar to be received in the future because funds received today can be invested to earn a return.

The time value of money states that the value of a dollar increases over a period of time because It can be invested to earn return on it. Thus a dollar received today can be invested to accumulate return and this will increase the worth of dollar

2

A) what one or more cash flows are worth at the end of a specified period.

Future value is the value of a cash flow received today at the end of specified period. It is the value of cash flow including the return earned for that specified period of time.

3)

C) Compounding.

Converting present value to future value involves adding the return on the present value. It is the process of compounding the return on return over a period of time.

4)

A) The higher the interest rate, the higher the future value of an investment

The future value is the sum of present value and the return earned on it over a period of time. Higher the interest rate means the return on the present value shall also be higher and also the future value.

5)

Present value (P) = $35,775

Quarterly rate of interest (r)= 4.75%/4 = 1.1875% = 0.011875

No. of compounding period (n) = 32 years *4 = 128

Future value = P*(1+r)ⁿ = $35,775 * 1.011875¹²⁸ = $162,113.20

Hence Answer is D) $162,113

6)

Present value (P) = $25,000

Rate of interest (r) = 6.25% = 0.0625

Compounding periods (n) = 20 years

Future value = $25,000*1.0625²⁰ = $84,046.34

Hence Answer is C) $84,046

7)

Present value (P) = $1,000,000

Daily Rate of interest (r) = 4.50%/365 = 0.012329% = 0.000123

Compounding periods (n) = 1 year * 365 = 365

Future value = $1,000,000 * 1.000123³⁶⁵ = $1,046,025

Hence Answer is D) $1,046,025

8)

Effective annual interest rate (EAR)= (1+ Annual rate/N)^N - 1, Where N is compounding frequency

3.50% compounding daily, EAR = (1+0.035/365)³⁶⁵ – 1 = 0.03562 =3.562%

3.25% compounding monthly, EAR = (1 + 0.0325/12)¹² – 1 = 0.03299 = 3.299%

3.40% compounded quarterly, EAR = (1 + 0.034/4)⁴ – 1 = 0.03444 = 3.444%

3.75% compounding annually, EAR = 3.75%

Hence, Answer is D) 3.75% compounded annually, with highest EAR

9)

Present value (P) = $2,500

Rate of interest (r) = 6% = 0.06

Compounding periods (n) = 5 years

Simple interest earned over 5 years = $2,500 * 0.06 * 5 = $750

Future value after 5 years under compounding interest = $2,500*1.06⁵ = $3,345.56

Compounding interest earned = Future value – Present value = $3,345.5 + $2,500 = $845,56

Interest on interest = $845.56 - $750 = $95.56

Hence, Answer is A)$750; $95.56

10)

Present value (P) = $3,000

Quarterly Rate of interest (r) = 5.25%/4 = 1.3125% = 0.013125

Compounding periods (n) = 4 years * 4 = 16

Simple interest earned over 5 years = $3,000 * 0.0525 * 4 = $630

Future value after 4 years under compounding interest = $3,000*1.013125¹⁶ = $3,695,.98

Compounding interest earned = Future value – Present value = $3,695.98 - $3,000 = $695.98

Interest on interest = $695.98 - $630 = $65.98

Hence Answer is B) $65.98