What is the future value of an ordinary annuity with annual payments of $1,000 for 4 years at 6% interest?

Question

Accepted Answer

$4,374.62. The future value of an ordinary annuity is calculated using FV = PMT x [(1+r)^n - 1] / r. FV = $1,000 x [(1.06)^4 - 1] / 0.06 = $1,000 x [1.26247696 - 1] / 0.06 = $1,000 x 0.26247696 / 0.06 = $1,000 x 4.374616 = $4,374.62 (rounded).

$4,000.00 represents simply the sum of four $1,000 payments without any interest, ignoring the time value of money entirely. $4,246.46 is less than the correct answer and may result from using a lower interest rate or fewer compounding periods in the calculation. $4,637.09 would result from calculating an annuity due (payments at the beginning of each period) rather than an ordinary annuity, since the annuity due future value equals the ordinary annuity future value multiplied by (1 + r): $4,374.62 x 1.06 = $4,637.10.

Annuity future value calculations are regularly tested on the DSST Business Mathematics exam. Students should memorize or be able to derive the ordinary annuity future value formula and understand how to use annuity factor tables. Recognizing whether a problem describes an ordinary annuity or annuity due is critical for selecting the correct calculation method.

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