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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.

 Jun 25, 2021
 #1
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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:   $2440.3+(0.052\times 2440.3)=\boxed{2567.2}$

 Jun 25, 2021
edited by UsernameTooShort  Jun 25, 2021

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