Question

You just graduated and landed your first job in your new career. You remember that your favorite finance professor told you to begin the painless job of saving for retirement as soon as possible, so you decided to put away $3,000 at the end of each year in a Roth IRA. Your expected annual rate of return on the IRA is 6.5%. How much will you accumulate at retirement after 40 years of investing (note: this may assume that you are even retiring early)?

a.

$694,426

b.

$647,921

c.

$526,896

d.

$454,513

Answer 1

Option (c) is correct

Here, the deposits will be same every year, so it is an annuity. We need to calculate the future value of annuity. 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 = $3000, r is the rate of interest = 6.5% and n is the time period = 40

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

FVA = $3000 * ((1 + 6.5%)40 - 1 / 6.5%)

FVA = $3000 * ((1 + 0.065)40 - 1 / 0.065)

FVA = $3000 * ((1.065)40 - 1 / 0.065)

FVA = $3000 * ((12.4160745337 - 1 / 0.065)

FVA = $3000 * (11.4160745337 / 0.065)

FVA = $3000 * 175.631915902

FVA = $526896

So, accumulated value after 40 years will be $526896.