Questions: Find the monthly payment needed to amortize principal and interest for the fixed-rate mortgage. Use either the regular monthly payment formula or the given table. Loan Amount Interest Rate Term 206,500 10% 25 years The monthly payment is (Round to the nearest cent as needed.)

Find the monthly payment needed to amortize principal and interest for the fixed-rate mortgage. Use either the regular monthly payment formula or the given table.
Loan Amount Interest Rate Term
206,500 10% 25 years

The monthly payment is
(Round to the nearest cent as needed.)

Transcript text: Find the monthly payment needed to amortize principal and interest for the fixed-rate mortgage. Use either the regular monthly payment formula or the given table. Loan Amount & Interest Rate & Term $\$ 206,500$ & $10 \%$ & 25 years The monthly payment is $\$$ $\square$ (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Convert the annual interest rate to a monthly interest rate

To find the monthly interest rate, divide the annual interest rate by 12. Given an annual interest rate of 10%, the monthly interest rate is 10/12 = 0.83%.

Step 2: Convert the term of the loan from years to months

The term of the loan is 25 years, which is equivalent to 25*12 = 300 months.

Step 3: Apply the mortgage payment formula

Using the formula $M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}$, where $P$ is the loan amount ($206500), $r$ is the monthly interest rate (0.83%), and $n$ is the total number of payments (300), we calculate the monthly payment.