Question

​Recently, More Money 4U offered an annuity that pays 5.7 % compounded monthly. If $1,011 is deposited into this annuity every​ month, how much is in the account after 6​years? (Round to the nearest dollar) Part 2 of the question: How much of this is​ interest? (Round to the nearest dollar)

Answer 1

Recall that the future value (FV), of an annuity payment of $P, for, n years at, t times a year at, r% interest compounded, t times a year is given by
$FV=P \frac{\left(1+ \frac{r}{t} \right)^{nt}-1}{\frac{r}{t}}$

Given that More Money 4U offered an annuity that pays r = 5.7% = 0.057 compounded monthly (12 times a year or t = 12). If P = $1,011 is deposited into this annuity every​ month (t = 12), then after n = 6 years the amount in the account is given by:
$FV=1,011\times \frac{\left(1+ \frac{0.057}{12} \right)^{6\times12}-1}{\frac{0.057}{12}} \\ \\ =1,011\times \frac{(1+0.00475)^{72}-1}{0.00475} =1,011\times \frac{(1.00475)^{72}-1}{0.00475} \\ \\ =1,011\times \frac{1.406621-1}{0.00475} =1,011\times \frac{0.406621}{0.00475} =1,011\times85.6044 \\ \\ =\ 86,546.05$

Therefore, the amount in the account after 6​years rounded to the nearest dollar is $86,546.


PART 2:
Given that $1,011 is deposited into this annuity every​ month for 6 years, the amount deposited into the account is given by
$1,011 x 12 x 6 = $72,792

Therefore, the amount of interest accrued is given by
$86,546 - $72,792 = $13,754

Therefore, the amount of interest received is $13,754