Nick and Jessica each have an annuity for their retirement N

Nick and Jessica each have an annuity for their retirement. Nick deposits $1200 each month into his account, with 5.50% interest compounded monthly. Jessica deposits $3200 each quarter into her account, with 6.25% interest compounded quarterly. If Nick must deposit money for 32 years and Jessica for 36 years, who will have the larger account in the future when they retire?

Solution

Solution:

Formula for calculating Future value of Annuity:

FV of Annuity = A * [{1 + (r/m)}^m*n - 1] / [(r/m)]

where A is Annuity amount

r is rate of interest

m is number of compounding periods per year

n is no. of years

Nick:

Let us first calculate amount that Nick would get at the time of retirement:

Since interest is compounded monthly, m = 12

FV of Annuity = A * [{1 + (r/m)}^m*n - 1] / [(r/m)]

FV of annuity = 1200 * [ {1 + (0.055/12)}^12*32 - 1] / [(0.055/12)]

                      = $ 1,253,876.652

Jessica:

Let us calculate amount that Jessica would get at the time of retirement:

Since interest is compounded quarterly, m = 4

FV of Annuity = A * [{1 + (r/m)}^m*n - 1] / [(r/m)

FV of annuity = 3200 * [{1 + (0.0625/4)}^4*36 -1] / (0.0625/4)]

                      = $1,704,776.473

Based on the above calculations, we can say that Jessica would have larger amount in futire at the time of retirement.