Respuesta :
The Brian paid amount of every quarter is $ 4287.79.
We have given that Brian took eight years to pay off his $ 71,900 loan, had an interest rate of 8.16%, compounded quarterly,
we have to determine, if Brian paid quarterly and made the same payment every time, how much was each payment that he made,
P=71900
r=8.16
[tex]r=\frac{8.16}{100}=0.0816[/tex]
[tex]i=\frac{r}{n}=\frac{0.0816}{4}= 1.0204[/tex]
for eight years
[tex]4\times 8=32[/tex]
What is the formula for the monthly payment?
[tex]monthly payment=P((1+i)^n/n)[/tex]
Where p=present value
r=interest rate
m=number of compounding periods
n=m(t)
t=times in years
i=r/m
Therefore by using the formula we get,
[tex](71900 \times (1 + 0.0816 / 4) ^ {4\times8}) / (8 \times 4) = X[/tex]
[tex](71900 \times 1.0204 ^ {32}) / 32 = X[/tex]
[tex](71900 \times 1.9083) / 32 = X[/tex]
[tex]137209.2177 / 32 = X[/tex]
[tex]4287.79 = X[/tex]
Therefore, Brian paid $ 4287.79 every quarter.
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