Question

Find the future value of an annuity due of $900 each quarter for 8 1/2 years at 10%, compounded quarterly. (Round your answer to the nearest cent.)

Answer 1

Answer : Calculation of future value of an annuity due :

Future Value of Annuity Due = Periodic Payment * {[(1 + r)^n - 1 ] / r } * (1 + r)

where r is the rate of interest per period i.e 10% / 4 = 2.5% or 0.025 (Divided by 4 as given compounded quarterly)

n is the number of periods i.e 8 1/2years = 8.5 year = 8.5 * 4 = 34 quaters (Multiplied by 4 as given compounded quarterly)

Periodic Payment i.e 900

Future Value of Annuity = 900 * {[(1 + 0.025)^34 - 1 ] / 0.025 } * (1 + 0.025)

= 900 * {[2.315322 - 1 ] / 0.025} * 1.025

= 900 * {1.315322 / 0.025} * 1.025

= 900 * 52.61289 * 1.025

= 48,535.39

= 44601.43

$44,601.43 will be accumulated by the end of year five.