**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

**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.

**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?

**Complete the following homework scenario:**

- Bob and Lisa are both married, working adults. They both plan for retirement and consider the $2,000 annual contribution a must.
- First, consider Lisa’s savings. She began working at age 20 and began making an annual contribution of $2,000 at the first of the year beginning with her first year. She makes 13 contributions. She worked until she was 32 and then left full time work to have children and be a stay at home mom. She left her IRA invested and plans to begin drawing from her IRA when she is 65.
Bob started his IRA at age 32. The first 12 years of his working career, he used his discretionary income to buy a home, upgrade the family cars, take vacations, and pursue his golfing hobby. At age 32, he made his first $2,000 contribution to an IRA, and contributed $2,000 every year up until age 65, a total of 33 years / contributions. He plans to retire at age 65 and make withdrawals from his IRA.

Both IRA accounts grow at a 7% annual rate. Do not consider any tax effect.

- Write a two to three (2-3) paragraph summary in which you:
- Create a chart summarizing the details of the investment for both Bob and Lisa.
- Explain the results in terms of time value of money.