An annuity pays $1200 per year for 15 years. The money is invested at 5.2% compounded annually. The first payment is made 1 year after the purchase of the annuity. Determine the interest earned by the annuity over the 15 years.
+171 there is a fixed formula for this ($\displaystyle{P}_{{m}}={\left({1}+\frac{{r}}{{k}}\right)}{P}_{{{m}-{1}}}$), but since we are not given the most important values, lets just do it all the way around and step by step so even you can have a better idea of how this works:
$1200$$+interess is going to get paid the 1st year
the 2nd year you will have to pay what you paid last year+interest of it
3rd year you is going to pay again what you got last year+interest
thus you get:
year 1 : $1200+(0.052\times 1200)=1262.4$
year 2: $ 1262.4+(0.052\times 1262.4)=1328$
year 3 : $ 1328+(0.052\times 1328)=1397$
year 4: $1397+(0.052\times 1397)=1470$
year 5: $1470+(0.052\times 1470)=1546.4$
year 6: $1546.4+(0.052\times 1546.4)=1328$
year 7: $1626.8+(0.052\times 1626.8)=1711.4$
year 8: $1711.4+(0.052\times 1711.4)=1800.4$
year 9: $1800.4+(0.052\times 1800.4)=1894$
year 10: $1894+(0.052\times 1894)=1992.5$
year 11: $1992.5+(0.052\times 1992.5)=2096$
year 12: $2096+(0.052\times 2096)=2205$
year 13: $2205+(0.052\times 2205)=2319.7$
year 14: $2319.7+(0.052\times 2319.7)=2440.3$
year 15: $2440.3+(0.052\times 2440.3)=\boxed{2567.2}$
