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There are three (3) types of textbook based homework items located at the end of each chapter. These include Discussion Questions (DQ), Exercises (E), and Problems (P). Some homework items have been custom created.

**Complete the following from the textbook:**

Chapter 9: E1, P2, P3, P4, P5, P7, P16, P17, P19

**1** Go to the Federal Reserve website, __http://www.federalreserve.gov__. Go to “Economic Research and Data,” and access “Consumer Credit.” Find interest rates charged by commercial banks on new automobile loans, personal loans, and credit card plans.

- Compare the current or recent level of interest rates among the three types of loans.
- Compare trends in the cost of consumer credit provided by commercial banks over the past three years.

**2** Go to the Federal Reserve website, __http://www.federalreserve.gov__. Go to “Economic Research and Data,” and access “Consumer Credit.” Determine current interest rates charged by finance companies versus commercial banks on new automobile loans. Also compare the cost of new automobile loans between finance companies and commercial banks over the past three years.

**3** Assume that your partner and you are in the consumer lending business. A customer, talking with your partner, is discussing the possibility of obtaining a $10,000 loan for three months. The potential borrower seems distressed and says he needs the loan by tomorrow or several of his relatively new appliances will be repossessed by the manufacturers. You overhear your partner saying that that in order to process the loan within one day there will be a $1,000 processing fee so that $11,000 in principal will have to be repaid in order to have $10,000 to spend now. Furthermore, because the money is needed now and is for only three months the interest charge will be 6 percent per month. What would you do?

**1** Find the future value one year from now of a $7,000 investment at a 3 percent annual compound interest rate. Also, calculate the future value if the investment is made for two years.

**2** Find the future value of $10,000 invested now after five years if the annual interest rate is 8 percent.

- What would be the future value if the interest rate is a simple interest rate?
- What would be the future value if the interest rate is a compound interest rate?

**3** Determine the future values if $5,000 is invested in each of the following situations:

- 5 percent for ten years
- 7 percent for seven years
- 9 percent for four years

**4** You are planning to invest $2,500 today for three years at a nominal interest rate of 9 percent with annual compounding.

- What would be the future value of your investment?
- Now assume that inflation is expected to be 3 percent per year over the same three-year period. What would be the investment’s future value in terms of purchasing power?
- What would be the investment’s future value in terms of purchasing power if inflation occurs at a 9 percent annual rate?

**5** Find the present value of $7,000 to be received one year from now, assuming a 3 percent annual discount interest rate. Also calculate the present value if the $7,000 is received after two years.

**6** Determine the present values if $5,000 is received in the future (i.e., at the end of each indicated time period) in each of the following situations:

- 5 percent for ten years
- 7 percent for seven years
- 9 percent for four years

**7** Determine the present value if $15,000 is to be received at the end of eight years and the discount rate is 9 percent. How would your answer change if you had to wait six years to receive the $15,000?

**8** Determine the future value at the end of two years of an investment of $3,000 made now and an additional $3,000 made one year from now if the compound annual interest rate is 4 percent.

**9** Assume you are planning to invest $5,000 each year for six years and will earn 10 percent per year. Determine the future value of this annuity if your first $5,000 is invested at the end of the first year.

**10** Determine the present value now of an investment of $3,000 made one year from now and an additional $3,000 made two years from now if the annual discount rate is 4 percent.

**11** What is the present value of a loan that calls for the payment of $500 per year for six years if the discount rate is 10 percent and the first payment will be made one year from now? How would your answer change if the $500 per year occurred for ten years?

**12** Determine the annual payment on a $500,000, 12 percent business loan from a commercial bank that is to be amortized over a five-year period.

**13** Determine the annual payment on a $15,000 loan that is to be amortized over a four-year period and carries a 10 percent interest rate. Also prepare a loan amortization schedule for this loan.

**14** You are considering borrowing $150,000 to purchase a new home.

- Calculate the monthly payment needed to amortize an 8 percent, fixed-rate, 30-year mortgage loan.
- Calculate the monthly amortization payment if the loan in (a) was for 15 years.

**15** Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan’s eight-year life.

- At what amount could this loan be sold for to another bank if loans of similar quality carried an 8.5 percent interest rate? That is, what would be the present value of this loan?
- Now, if interest rates on other similar-quality loans are 10 percent, what would be the present value of this loan?
- What would be the present value of the loan if the interest rate is 8 percent on similar-quality loans?

**16** Use a financial calculator or computer software program to answer the following questions:

- What would be the future value of $15,555 invested now if it earns interest at 14.5 percent for seven years?
- What would be the future value of $19,378 invested now if the money remains deposited for eight years and the annual interest rate is 18 percent?

**17** Use a financial calculator or computer software program to answer the following questions:

- What is the present value of $359,000 that is to be received at the end of 23 years if the discount rate is 11 percent?
- How would your answer change in (a) if the $359,000 is to be received at the end of 20 years?

**18** Use a financial calculator or computer software program to answer the following questions:

- What would be the future value of $7,455 invested annually for nine years beginning one year from now if the annual interest rate is 19 percent?
- What would be the present value of a $9,532 annuity for which the first payment will be made beginning one year from now, payments will last for 27 years, and the annual interest rate is 13 percent?

**19** Use a financial calculator or computer software program to answer the following questions.

- What would be the future value of $19,378 invested now if the money remains deposited for eight years, the annual interest rate is 18 percent, and interest on the investment is compounded semi-annually?
- How would your answer for (a) change if quarterly compounding were used?

**20** Use a financial calculator or computer software program to answer the following questions.

- What is the present value of $359,000 that is to be received at the end of 23 years, the discount rate is 11 percent, and semi-annual discounting occurs?
- How would your answer for (a) change if monthly discounting were used?

**21** What would be the present value of a $9,532 annuity for which the first payment will be made beginning one year from now, payments will last for 27 years, the annual interest rate is 13 percent, quarterly discounting occurs, and $2,383 is invested at the end of each quarter?

**22** Answer the following questions.

- What is the annual percentage rate (APR) on a loan that charges interest of .75 percent per month?
- What is the effective annual rate (EAR) on the loan described in (a)?

**23** You have recently seen a credit card advertisement stating that the annual percentage rate is 12 percent. If the credit card requires monthly payments, what is the effective annual rate of interest on the loan?

**24** A credit card advertisement states that the annual percentage rate is 21 percent. If the credit card requires quarterly payments, what is the effective annual rate of interest on the loan?

**25** **Challenge Problem** [Note: A computer spreadsheet software program or a financial calculator that can handle uneven cash flow streams will be needed to solve the following problems.] The following cash flow streams are expected to result from three investment opportunities.

Year | Investment Stable | Investment Declining | Investment Growing |

1 | $20,000 | $35,000 | $10,000 |

2 | 20,000 | 30,000 | 15,000 |

3 | 20,000 | 20,000 | 20,000 |

4 | 20,000 | 5,000 | 30,000 |

5 | 20,000 | 0 | 50,000 |

- Find the present values at the end of time period zero for each of these three investments if the discount rate is 15 percent. Also, find the present values for each investment using 10 percent and 20 percent discount rates.
- Find the future values of these three investments at the end of year five if the compound interest rate is 12.5 percent. Also, find the future values for each investment using 2.5 percent and 22.5 percent compound rates.
- Find the present values of the three investments using a 15 percent annual discount rate but with quarterly discounting. Also, find the present values for both semi-annual and monthly discounting for a 15 percent stated annual rate.
- Find the future values of the three investments using a 12.5 percent annual compound rate but with quarterly compounding. Also find the future values for both semi-annual and monthly compounding for a 12.5 percent stated annual rate.
- Assume that the present value for each of the three investments is $75,000. What is the annual interest rate (%i) for each investment?
- Show how your answers would change in (e) if quarterly discounting takes place.
- Assume that the future value for each of the three investments is $150,000. What is the annual interest rate (%i) for each investment? [Note: (e) and (g) are independent of each other.]
- Show how your answers would change in (g) if quarterly compounding takes place.

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