Question

Angelica has been depositing $280 each month into a savings account with an APR of 2.76% for the last 3 years. If she continues depositing this amount for an additional 12 years, what will the balance in her savings account be?

Answer 1

$62,490.65

Explanation:

If we assume her deposits are at the beginning of the month, and that the interest is compounded monthly, the future value is that of an "annuity due." The formula is ...

FV = P(1+r/n)((1+r/n)^(nt)-1)/(r/n)

where r is the APR (.0276), n is the number of yearly compoundings (12), P is the monthly payment ($280), and t is the number of years (15). Putting the numbers into the formula and doing the arithmetic, we get ...

FV = $280(1.0023)(1.0023^180 -1)/(.0023) ≈ $62,490.65

Angelica's account balance after 15 years will be $62,490.65.

_____

If her deposits are at the end of the month, the balance will be $62,347.25.