Problem 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.
Problem 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.
Problem 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?
Problem 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?
Problem 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.
Problem 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.
Problem 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?