Mariam starts saving for retirement at age 29. If she deposits $950 each month in an account that pays 7.8% interest, how much has Mariam saved by the time she retires at age 62?

Question

$1,755,217
$134,919
$376,200
$12,359
$381,071

Answer 1

The formula to calculate the future value of an annuity is:

FV = Pmt * [(1 + r)^n - 1] / r

Where:
FV = Future Value
Pmt = Monthly deposit amount = $950
r = Monthly interest rate = Annual interest rate / 12 = 7.8% / 12 = 0.65% or 0.065
n = Number of months = (62 - 29) * 12 = 396

Now, plugging in the values:

FV = $950 * [(1 + 0.065)^396 - 1] / 0.065
FV = $950 * [(1.065)^396 - 1] / 0.065
FV = $950 * [349.826 - 1] / 0.065
FV = $950 * 348.826 / 0.065
FV = $1,755,217

Therefore, by the time Mariam retires at age 62, she would have saved $1,755,217. So, the answer is $1,755,217.