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
[tex]FV=P \frac{\left(1+ \frac{r}{t} \right)^{nt}-1}{\frac{r}{t}} [/tex]
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:
[tex]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[/tex]
Therefore, the amount in the account after 6years 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
