# Work Shown for All

1. Ben Woolmer has an investment that will pay him the following cash flows over the next five years: \$8,061, \$4,266, \$9,547, \$4,399, and \$7,327. If his investments typically earn 9.72 percent, what is the future value of the investment’s cash flows at the end of five years?

2. Saul Cervantes has just purchased some equipment for his landscaping business. For this equipment he must pay the following amounts at the end of each of the next five years: \$11,009, \$13,949, \$8,595, \$9,780, and \$12,151. If the appropriate discount rate is 13.332 percent, what is the cost in today’s dollars of the equipment Saul purchased today?

3. Calculate effective annual interest rate (EAR) for the following investments.
a. A bank CD that pays 8.13 percent compounded quarterly. Calculate effective annual interest rate (EAR)?
b. A bank CD that pays 8.13 percent compounded monthly. Calculate effective annual interest rate (EAR)?
c. A bank CD that pays 8.33 percent compounded annually. Calculate effective annual interest rate (EAR)?
d. A bank CD that pays 8.13 percent compounded semi-annually. Calculate effective annual interest rate (EAR)?
e. A bank CD that pays 7.88 percent compounded daily (on a 365-day basis). Calculate effective annual interest rate (EAR)?
f. Which of the above investments has the highest effective annual interest rate (EAR)?

4. Dynamics Telecommunications Corp. has made an investment in another company that will guarantee it a cash flow of \$21,768 each year for the next five years. If the company uses a discount rate of 20 percent on its investments, what is the present value of this investment?

5. Cecelia Thomas is a sales executive at a Baltimore firm. She is 25 years old and plans to invest \$2,558 every year in an IRA account, beginning at the end of this year until she turns 65 years old. If the IRA investment will earn 8.03 percent annually, how much will she have in 40 years, when she turns 65?

6. Kevin Winthrop is saving for an Australian vacation in three years. He estimates that he will need \$5,939 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average return of 10.1 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year?

7. Modern Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility they are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of \$95,020 last year, and the current owners expect an annual growth rate of 6.3 percent. If Modern Energy uses a discount rate of 17.1 percent to evaluate such businesses, what is the present value of this growing annuity?

8. Cyclone Rentals borrowed \$15,550 from a bank for three years. If the quoted rate (APR) is 8.37 percent, and the compounding is daily, what is the effective annual interest rate (EAR)?

9. Calculate the annual cash flows for each of the following investments:
a. \$246,624 invested at 6 percent.
b. \$37,117 invested at 12 percent.
c. \$77,534 invested at 10 percent.