Question

A 42​-year-old man puts ​$1500 in a retirement account at the end of each quarter until he reaches the age of 61​, then makes no further deposits. If the account pays 4​% interest compounded​ quarterly, how much will be in the account when the man retires at age 66​? There will be how much $ in the account. Round to the nearest cent

Answer 1

Here, the deposits will be same every quarter, so it is an annuity. We need 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 = $1500, r is the rate of interest = 4% compounded quarterly, so quarterly rate = 4% / 4 = 1%  and n is the time period = 19 years or 19 * 4 = 76 quarters

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

FVA = $1500 * ((1 + 1%)76 - 1 / 1%)

FVA = $1500 * ((1 + 0.01)76 - 1 / 0.01)

FVA = $1500 * ((1.01)76 - 1 / 0.01)

FVA = $1500 * ((2.13021975304 - 1 / 0.01)

FVA = $1500 * (1.13021975304 / 0.01)

FVA = $1500 * 113.021975304

FVA = $169532.96

So, there will be $169532.96 in the account.