Question: 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

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 and add 1 to the tabular value. To find the present value of an annuity due, the annuity formula must be adjusted as to the following:

Likewise, the formula for the future value of an annuity due requires a modification:

What is the future value of a 15-year annuity of $1,800 per period where payments come at the beginning of each period? The interest rate is 12 percent.

1-. (1+i)*-T +1 PV = Ax

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