Respuesta :
The total interest earned on the annuity is $243,548.50
What is annuity?
An annuity is a situation where the same amount is invested periodically, in this an amount is invested every six months for 25 years.
The $500,000 is the future value of the annuity , which means we can determine semiannual payment using the future value formula provided below:
FV=semiannual payment*(1+r)^N-1/r
FV=future value=$500,000
semiannual payment=unknown(assume it is X)
r=semiannual interest rate=5%/2=0.025
N=number of semiannual payments in 25 years=25*2=50
$500,000=X*(1+0.025)^50-1/0.025
$500,000=X*(1.025)^50-1/0.025
$500,000=X*(3.43710871970354-1)/0.025
$500,000=X*2.43710871970354/0.025
$500,000=X*97.48434878814160
X=$500,000/97.48434878814160
X=$5,129.03
Total interest=future value-total invested
total invested=semiannual payment*50
total invested=$5,129.03*50
total invested=$256,451.50
total interest=$500,000-$256,451.50
total interest=$243,548.50
Find out more about annuity on:https://brainly.com/question/25792915
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