Respuesta :
We have a purchase at a price of $997.
The downpayment is 10%, so it represents $99.70
[tex]\text{downpayment}=\frac{10}{100}\cdot997=0.1\cdot997=99.70[/tex]Then, the amount that is financed is:
[tex]997-99.70=897.30[/tex]We then can calculate the monthly payments using the annuity formula.
As there are monthly payments, we have to calculate a monthly interest rate:
[tex]r_m=\frac{r}{12}=\frac{0.10}{12}\approx0.0083[/tex]Then, the monthly payment will be:
[tex]\begin{gathered} A=\frac{897.30}{\frac{1}{r_m}-\frac{1}{r_m(1+r_m)^n}} \\ A=\frac{897.30}{\frac{12}{0.1}-\frac{1}{\frac{0.1}{12}(1+\frac{0.1}{12})^{36}}} \\ A=\frac{897.30}{120-\frac{1}{0.0083\cdot(1.0083)^{36}}} \\ A=\frac{897.30}{120-\frac{1}{0.0083\cdot1.348}} \\ A=\frac{897.30}{120-89.38} \\ A=\frac{897.30}{30.62} \\ A=29.30 \end{gathered}[/tex]We can calculate the total financed payments as:
[tex]A\cdot n=29.30\cdot36=1054.80[/tex]The finance charge will be the difference between the total financed payments and the financed value:
[tex]I=1054.80-897.30=157.50[/tex]Answer: Finance charge = $157.50
