# For each of the following, compute the present value

1. First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually.

If you made a $60,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years? **(Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))**

** Difference in accounts __$?**

2. For each of the following, compute the future value** (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))**:

Present Value Years Interest Rate **Future Value **

$1,950 10 14 % $___?___

$8,152 8 8% $___?___

$70,355 15 13% $___?___

$177,796 6 5% $___?___

**3. **For each of the following, compute the present value **(Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))**:

**Present Value **Years Interest Rate Future Value

$_____ 12 6 % $14,751

$_____ 3 12% $44,557

$_____ 28 13% $879,073

$_____ 30 10 % $543,164

4. Solve for the unknown interest rate in each of the following **(Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))**:

Present Value Years **Interest Rate** Future Value

$170 3 __ % $196

$290 17 __% $732

$32,000 18 __% $124,723

$31,261 20 __ % $226,140

5.Solve for the unknown number of years in each of the following

Present Value **Years** Interest Rate Future Value

$510 __ 9 % $1,212

$760 __ 10% $1,629

$17,900 __ 17% $260,563

$21,000 __ 15 % $391,887

6. Assume the total cost of a college education will be $250,000 when your child enters college in 17 years. You presently have $62,000 to invest.

What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? **(Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))**

** Annual rate of interest ___% ?**

7**. **At 5.70 percent interest, how long does it take to double your money? **(Round your answer to 2 decimal places. (e.g., 32.16))**

** Length of time ____ years ?**

At 5.70 percent interest, how long does it take to quadruple it? **(Round your answer to 2 decimal places. (e.g., 32.16))**

** Length of time ____ years ? **

8. Assume that in January 2010, the average house price in a particular area was $277,400. In January 2001, the average price was $194,300.

What was the annual increase in selling price? **(Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))**

** Annual increase in selling price ___ % ? **

9. You’re trying to save to buy a new $194,000 Ferrari. You have $44,000 today that can be invested at your bank. The bank pays 5.2 percent annual interest on its accounts.

How long will it be before you have enough to buy the car?

** Number of years ____ ? **

10. Imprudential, Inc. has an unfunded pension liability of $572 million that must be paid in 25 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present.

If the relevant discount rate is 6.5 percent, what is the present value of this liability? **(Enter your answer in dollars not in millions. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))**

** Present value $ _____ ? **

11. You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 74 years from now.

What is the present value of your windfall if the appropriate discount rate is 9 percent?

** **

** Present value $____ ? **

12. Your coin collection contains 44 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2054, assuming they appreciate at a 5.7 percent annual rate?

** Future value $___ ? **

13. In 1895, the first Putting Green Championship was held. The winner’s prize money was $180. In 2010, the winner’s check was $1,380,000.

What was the percentage increase per year in the winner’s check over this period?

** Interest rate ____ % ? **

If the winner’s prize increases at the same rate, what will it be in 2037?

** Future value ____ $ ? **

14. Assume that in 2010, a gold dollar minted in 1893 sold for $127,000. For this to have been true, what rate of return did this coin return for the lucky numismatist?

** Rate of return _____ % ? **

15. Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, an auction house sold a sculpture at auction for a price of $10,361,500. Unfortunately for the previous owner, he had purchased it in 2000 at a price of $12,477,500.

What was his annual rate of return on this sculpture? **(Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))**

** Annual rate of return _____ % ? **

1b. Wainright Co. has identified an investment project with the following cash flows.** **

Year Cash Flow

1$740

2$970

3$1,230

4$1,325

** **

If the discount rate is 9 percent, what is the present value of these cash flows?

**Present Value $ ______ ? **

What is the present value at 18 percent?

** Present value $ ____ ? **

** **

What is the present value at 24 percent?

** Present value $ ____ ? **

2. Investment X offers to pay you $4,200 per year for seven years, whereas Investment Y offers to pay you $6,300 per year for four years.

Calculate the present value for Investment X and Y if the discount rate is 6 percent.

**Present value**

** Investment X$ ______?**

** Investment Y$ ______?**

Calculate the present value for Investment X and Y if the discount rate is 16 percent.

**Present value**

** Investment X$ ____?**

** Investment Y$ ____?**

3. Toadies, Inc., has identified an investment project with the following cash flows.

YearCash Flow

1$1,625

2$1,745

3$1,830

4$1,880

If the discount rate is 9 percent, what is the future value of the cash flows in year 4?

** Future value$ _____ ? **

If the discount rate is 10 percent, what is the future value of the cash flows in year 4?

** Future value$ _____ ? **

If the discount rate is 25 percent, what is the future value of the cash flows in year 4?

** Future value$ _____ ? **

**4. **First Simple Bank pays 8.2 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?

** Interest rate _____ % ? **

**5. **Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $6,600, $11,600, and $17,800 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 13 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?

- $27,261.50
- b. $39,420.00

c. $28,896.22

d. $36,000.00

e. $24,876.50

6. One year ago, the Jenkins Family Fun Center deposited $5,200 in an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $7,000 to this account. They plan on making a final deposit of $9,200 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a 6 percent rate of return?

a. $25,438.74

b. $26,753.46

c. $25,993.97

d. $24,234.57

- $25,495.73

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