Question

Jane Adele deposits $700 in an account at the beginning of each 3-month period for 9 years. If the account pays interest at the rate of 12%, compounded quarterly, how much will she have in her account after 9 years? (a) State whether the problem relates to an ordinary annuity or an annuity due. (b) Solve the problem. (Round your answer to the nearest cent.)

Answer 1

The problem relates to an annuity due as the inflows occur at the beginning of each period.

The future value ($ F) of an annuity due is given by F = (P/r)* (1+r) *[(1+r)ⁿ-1], where P is the periodic payment , r is the rate per period and n is the number of periods.

Here, P = $ 700, n = 4*9 = 36 and r = 12/400 = 0.03 so that F = (700/0.03)*(1.03) *[ (1.03)³⁶-1] = (700/0.03)*(1.03) *1.898278328 = $ 45621.96 ( on rounding off to the nearest cent).

Thus, Jane Adele will have $ 45621.96 in her account after 9 years.