An investment offers to triple your money in 24

Chapter 6 homework 3 image1.wmf

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1. An investment offers $7,100 per year for 20 years, with the first payment occurring one year from now.

If the required return is 7 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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What would the value be if the payments occurred for 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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2. If you put up $44,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Annual cash flow

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3. If you deposit $5,500 at the end of each of the next 15 years into an account paying 11.30 percent interest, how much money will you have in the account in 15 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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How much will you have if you make deposits for 30 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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4. You want to have $74,000 in your savings account 11 years from now, and you’re prepared to make equal annual deposits into the account at the end of each year. If the account pays 6.30 percent interest, what amount must you deposit each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Deposit amount

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5. The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $29,000 per year forever. If the required return on this investment is 5.30 percent, how much will you pay for the policy? (Round your answer to 2 decimal places. (e.g., 32.16))

Present value

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6. The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $20,000 per year forever. Suppose a sales associate told you the policy costs $465,000. At what interest rate would this be a fair deal? (Round your answer to 2 decimal places. (e.g., 32.16))

Interest rate

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%

7. Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Stated Rate (APR)

Number of Times Compounded

Effective Rate (EAR)

9.8

%

Quarterly

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%

18.8

Monthly

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14.8

Daily

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11.8

Infinite

image16.wmf

8. Find the APR, or stated rate, in each of the following cases (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

Stated Rate (APR)

Number of Times Compounded

Effective Rate (EAR)

image17.wmf

%

Semiannually

11.2

%

image18.wmf

Monthly

12.1

image19.wmf

Weekly

9.8

image20.wmf

Infinite

13.5

9. First National Bank charges 14.2 percent compounded monthly on its business loans. First United Bank charges 14.5 percent compounded semiannually.

Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

EAR

First National

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%

First United

image22.wmf

%

As a potential borrower, which bank would you go to for a new loan?

image23.wmf

First National Bank

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First United Bank

10. Barcain Credit Corp. wants to earn an effective annual return on its consumer loans of 14.1 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Interest rate

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%

Chapter 6 homework 4

11. What is the future value of $1,900 in 18 years assuming an interest rate of 7.2 percent compounded semiannually? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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12. Gold Door Credit Bank is offering 6.3 percent compounded daily on its savings accounts. You deposit $4,700 today.

How much will you have in the account in 4 years? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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How much will you have in the account in 12 years? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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How much will you have in the account in 19 years? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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13. An investment will pay you $35,000 in 10 years. If the appropriate discount rate is 6.2 percent compounded daily, what is the present value? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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14. You want to buy a new sports coupe for $84,500, and the finance office at the dealership has quoted you a 6.6 percent APR loan for 48 months to buy the car.

What will your monthly payments be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Monthly payment

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What is the effective annual rate on this loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective annual rate

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%

.

15. You are planning to make monthly deposits of $310 into a retirement account that pays 9 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 35 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Future value

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16. You are planning to make annual deposits of $6,330 into a retirement account that pays 10 percent interest compounded monthly. How large will your account balance be in 28 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

FVA

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17. The appropriate discount rate for the following cash flows is 8 percent compounded quarterly.

Year

Cash Flow

1

$

900

2

980

3

0

4

1,570

What is the present value of the cash flows? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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18. The appropriate discount rate for the following cash flows is 7.58 percent per year.

Year

Cash Flow

1

$

2,520

2

0

3

3,960

4

2,210

What is the present value of the cash flows? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

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19. You are looking at an investment that has an effective annual rate of 14.6 percent.

What is the effective semiannual return? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective semiannual return

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%

What is the effective quarterly return? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective quarterly return

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%

What is the effective monthly return? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective monthly return

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%

20. You want to be a millionaire when you retire in 35 years.

How much do you have to save each month if you can earn an 11.8 percent annual return? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Savings per month

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How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Savings per month

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How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Savings per month

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21. Suppose an investment offers to triple your money in 36 months (don’t believe it). What rate of return per quarter are you being offered? (Round your answer to 2 decimal places. (e.g., 32.16))

Rate of return

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%

22. Given an interest rate of 4.2 percent per year, what is the value at date t = 7 of a perpetual stream of $2,600 payments that begins at date t = 15? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Perpetuity value

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