Question

Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if ​$10 is invested semiannually for 20 years at 6.5​% compounded semiannually. The accumulated amount will be

Answer 1

solution:

The formula for computing the maturity value (A) of an ordinary annuity is A = p[ (1+r/n)^nt -1]/(r/n), where p is the payment per period , r is the rate of interest in decimals, n is the number of times, the interest is compounded in an year and t is the number of years.

Here, p = $ 10, n = 2, r = 6.5 /100 = 0.065 and t=20.

Hence, A=10[(1+0.065/2)^2*20]/(0.065/2)

=10[(1+0.0325)^40-1]/(0.065/2)

= $ 798.2158 ( on rounding off to the nearest cent).

Thus, the required accumulated amount is $ 798.22