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 at the beginning of each period

(termed an annuity due). To find the present value of an annuity due, subtract 1 from n an add | to the tabular value. To find the future value of an annuity, add 1 to n and subtract | from the tabular value. For example, to find the future value of a $100 payment at the beginning of each period for five periods at 10 percent, go to Appendix C for n = 6 andi = 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.

Related to the discussion in problem 23, what is the present 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.