# 7 annuity payments problems

1. As stated in the chapter, annuity payments are assumed to come at the end of each payment period (termed an ordinary annuity). However, an exception occurs when the annuity payments come in the beginning of each period (termed an annuity due). To find the present value of an annuity due, subtract 1 from n an add 1 to the tabular value. For example, to find the future future percent, go to Appendix C for n = 6 and i = 10 percent. Look up the value of 7.716 and subtract 1 from it for an answer of 6.716 or $671.60 ($100 x 6.716).

What is the future value of a 10-year annuity of $2,000 per period where payments come at the beginning of each period? The interest rate is 8 percent.

2. Related to the discussion in problem 23, what is the percent value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent.

3. You need $23,956 at the end of nine year, and your only investment outlet is a 7 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.

a. What single payment could be made at the beginning of the first year to achieve this object?

b. What amount could you pay ay the end of each year annually for nine years to achieve this same objective?

4. Beverly Hills started a paper route on January 1, 2001. Every three months, she deposits $300 in her bank account, which earns 8 percent annually but is compounded quarterly. On December 31, 2004, she used the entire balance in her bank account to invest in an investment at 12 percent annually. How much will she have on December 31, 2007?

5. On January 1, 2005, Mr. Dow bought 100 shares of stock at $12 per share. On December 31, 2008, he sold the stock for $18 per share. What is his annual rate on return? Interpolate to find the answer.

6. C. D. Rom has just given an insurance company $30,000. In return, he will receive an annuity of $3,200 for 20 years.

At what rate of return must the insurance company invest this $30,000 in order to make the annual payments? Interpolate.

7. Rusty Steele will receive the following payments at the end of the next three years: $4,00. $7,000, and $9,000. Then from the end of the fourth year through the end of the tenth year, he will receive an annuity of $10,000. At a discount rate of 10 percent, what is the present value of all future benefits?

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Student,

I don't have the tables you reference and the exact definition ...

#### Solution Summary

7 annuity payments problems solved step-by-step in an attached PDF covering annuities due, compound interest, ordinary annuities, and the deferred annuity. This is an algebraic solution and analysis, not an implementation in Excel.

Time Value of Money and Capital Budgeting

Problem: If you invest $8000 per period for the following number of periods, how much would you have?

a.7 years at 9 percent

b.40 years at 11 percent

Problem: The western sweeptakes has just informed you that you have won $1 million. The amount is to be paid at the rate of $50000 a year for the next 20 years. With a discount rate of 12%, what is the present value of your winnings.

Problem: Dr Oats, a nutrition professor, invests $8000 in a piece of land that is expected to increase in value by 14% per year for the next five years. She will then take the proceeds and provide herself with a 10-year annuity. Assuming a 14 percent interest rate for the annuity, how much will this annuity be?

Problem: Essex Biochemical Company has a $1000 par value bond that pays 10 percent annual interest. The company yield to maturity on such bonds in the market is 7 percent. Compute the price of the bonds for these maturity dates:

a.30 years

b.15 years

c.1 year

Problem: Bonds issued by Coleman Manufacturing Company have a par value of $1,000, which, of course, is also the amount of principal to be paid at maturity. The bonds are currently selling for $850. They have 10 years remaining to maturity. The annual interest payment is 8 percent ($80). Compute the approximate yield to maturity.

Problem: Laser optics will pay a common stock dividend of $1.60 at the end of year (D1). The required rate of return on common stock (Ke) is 13%. The firm has a constant growth rate(g) of 7 percent. Compute the current price of the stock(Po).

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