Questions: Question 13 10 pts Determine the monthly principal and interest payment for a 20-year mortgage when the amount financed is 365,111 and the annual percentage rate (APR) is 5.4%. Round to the nearest cent (2 decimal places).

Question 13
10 pts

Determine the monthly principal and interest payment for a 20-year mortgage when the amount financed is 365,111 and the annual percentage rate (APR) is 5.4%.

Round to the nearest cent (2 decimal places).

Transcript text: Question 13 10 pts Determine the monthly principal and interest payment for a 20-year mortgage when the amount financed is $\$ 365,111$ and the annual percentage rate (APR) is 5.4\%. Round to the nearest cent ( 2 decimal places). $\square$

Solution

Solution Steps

Step 1: Convert the annual rate to a monthly rate and the term in years to months

To find the monthly payment, we first convert the annual percentage rate (APR), 5.4%, to a monthly rate by dividing by 1200. This gives us $r' = \frac{5.4}{1200} = 0.0045$. Next, we convert the term of the mortgage from years to months by multiplying by 12. So, $n' = n \times 12 = 240$ months.

Step 2: Apply the mortgage payment formula

The monthly payment $M$ can be calculated using the formula: \[M = P \frac{r'(1 + r')^{n'}}{(1 + r')^{n'} - 1}\] Substituting the values, we get $M = 365111 \times \frac{0.0045 \times (1 + 0.0045)^{240}}{(1 + 0.0045)^{240} - 1} = 2490.98$.