Respuesta :
First, we calculate how much is 17% of the home cost $200,00. For this, we divide 200,000 by 100 and then multiply by 17:
[tex]\frac{200,000}{100}\times17=34,000[/tex]The down payment was $34,000
So we subtract this amount from the total amount of the home:
[tex]200,000-34,000=166,000[/tex]They still need to pay $166,000.
Now we use the mortgage formula to calculate the monthly payments "M":
[tex]\begin{gathered} M=P\times\frac{r(1+r)^n}{(1+r^{})^n-1} \\ \end{gathered}[/tex]Where P is the principal or the amount borrowed. In this case:
[tex]P=166,000[/tex]n is the number of payments. Since the payments are monthly for 15 years, and each year has 12 months. The amount of payments n is:
[tex]n=15\times12=180[/tex]And r is the interest rate divided by 12. The interest rate is 3.84% which in decimal is 0.0384. Thus, the value of r is:
[tex]r=\frac{0.0384}{12}=0.0032[/tex]We substitute all of these values into the formula:
[tex]M=166,000\times\frac{0.0032(1+0.0032)^{180}}{(1+0.0032)^{180}-1}[/tex]Solving the operations to find M:
[tex]\begin{gathered} M=166,000\times\frac{0.0032(1.0032)^{180}}{(1.0032)^{180}-1} \\ M=166,000\times\frac{0.0032(1.7773)^{}}{1.7773^{}-1} \\ M=166,000\times\frac{5.687\times10^{-3}^{}}{0.7773^{}} \\ M=1,214.57 \end{gathered}[/tex]The monthly payments: $1,214.57
If they increase the monthly payment to 1300, we need to divide the 166,000 by 1,300 to find the number of payments they have to make:
[tex]\frac{166,000}{1300}=127.7[/tex]The number of payments: 127.7
