Calculate the monthly payments of a 30-year fixed-rate mortgage at 5.25 percent for $139,700. How much interest is paid over the life of the loan? The monthly payments of a 30-year fixed-rate mortgage at 5.25% for $139,700 is
The correct answer and explanation is :
To calculate the monthly payments for a 30-year fixed-rate mortgage of $139,700 at an interest rate of 5.25%, we can use the mortgage payment formula:
[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n – 1}
]
Where:
- (M) is the monthly payment.
- (P) is the principal loan amount ($139,700).
- (r) is the monthly interest rate (annual interest rate divided by 12). For 5.25%, the monthly rate is ( \frac{5.25}{100 \times 12} = 0.004375 ).
- (n) is the total number of payments (loan term in years multiplied by 12). For a 30-year mortgage, (n = 30 \times 12 = 360).
Step 1: Calculate the Monthly Payment
We will substitute the values into the mortgage payment formula:
[
M = 139700 \times \frac{0.004375(1 + 0.004375)^{360}}{(1 + 0.004375)^{360} – 1}
]
Now, calculating:
[
M \approx 139700 \times \frac{0.004375(5.138)}{5.138 – 1}
]
[
M \approx 139700 \times \frac{0.0225}{4.138}
]
[
M \approx 139700 \times 0.00544
]
[
M \approx 759.29
]
So, the monthly payment is approximately $759.29.
Step 2: Calculate the Total Interest Paid Over the Life of the Loan
The total amount paid over 30 years is:
[
\text{Total Payments} = M \times n = 759.29 \times 360 \approx 273,344.40
]
Now, subtract the principal loan amount from the total payments to find the total interest paid:
[
\text{Total Interest} = \text{Total Payments} – \text{Principal} = 273,344.40 – 139,700 = 133,644.40
]
Summary
- Monthly Payment: $759.29
- Total Interest Paid Over the Life of the Loan: $133,644.40
This means that over 30 years, you will pay $133,644.40 in interest on top of the original loan amount of $139,700.