Respuesta :
Step 1- Write out the Present Value of Annuity formula:
[tex]PV=P\times\frac{1-(1+\frac{r}{n})^{-t\times n}}{\frac{r}{n}}[/tex]Where
[tex]\begin{gathered} PV=\text{ the present value} \\ P=\text{ the periodic payment} \\ n=\text{ the number of payments in a year} \\ r=\text{ annual interest rate} \end{gathered}[/tex]Step 2- Write out the given values and substitute them into the formula:
[tex]\begin{gathered} PV=\$26232(1-0.1)=\$26232\times0.9=\$23608.80 \\ n=12 \\ r=0.075 \end{gathered}[/tex]Substituting the values into the formula, we have:
[tex]23608.80=P\times\frac{1-(1+\frac{0.075}{12})^{-8\times12}}{\frac{0.075}{12}}[/tex]Therefore,
[tex]23608.80=72.0260P[/tex]Dividing both sides by 72.0260, we have:
[tex]P=\$327.78[/tex]Hence, the monthly payment is $327.78.
The total amount T paid is given by:
[tex]T=\$327.78\times8\times12=\$31466.88[/tex]Hence, the interest I is given by:
[tex]I=31466.88-23608.80=\$7858.08[/tex]Therefore, the monthly payment is $327.78 and the interest paid is $7858.08
