Question

Leo did not start saving for his retirement when he started working. Instead, he waited until age forty. Now he only has 26 years to save for retirement. Assume that he puts the $300 per month into his IRA. At a 9.8% average annual return how much would have Leon have for contributions made at the end of the month?

a. $459,681.63

b. $443,500.73

c. 427,956.75

d. $459,681.63

Answer 1

Option (c) is correct

Here, the deposits will be same every month, so it is an annuity. We have to find the future value of annuity here. We will use the future value of annuity formula as per below:

FVA = P * ((1 + r)n  - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $300, r is the rate of interest = 9.8% compounded monthly, so monthly rate = 9.8% / 12 = 0.816667%  and n is the time period = 26 * 12 = 312 months

Now, putting these values in the above formula, we get,

FVA = $300 * ((1 + 0.816667%)312- 1 / 0.816667%)

FVA = $300 * ((1 + 0.00816667)312 - 1 / 0.00816667)

FVA = $300 * ((1.00816667)312 - 1 / 0.00816667)

FVA = $300 * ((12.6499336206 - 1 / 0.00816667)

FVA = $300 * (11.6499336206 / 0.00816667)

FVA = $300 * 1426.52242593

FVA = $427956.75

So, Leon will have $427956.75.