Final answer:
To compare the monthly payments for a 25-year, $120,000 home loan at 6 1/2% and 8%, calculate the monthly payment for each rate using the mortgage formula and then subtract the lower payment from the higher one to find the difference.
Step-by-step explanation:
To determine the difference between the monthly payments on a $120,000 home at 6 1/2% and at 8% interest rates for a term of 25 years, we can use the formula for calculating the fixed monthly mortgage payments:
The formula for the monthly payment of a mortgage is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n − 1 ]
Where:
- M is your monthly payment.
- P is the principal loan amount ($120,000 in this case).
- i is your monthly interest rate.
- n is your number of payments (the number of months you will be paying the loan).
First, we need to convert the annual interest rates to monthly rates by dividing by 12 (since there are 12 months in a year). Next, we multiply the number of years by 12 to find 'n', the total number of payments. Then we can plug these values into the formula to find the monthly payment for each interest rate.
For a rate of 6 1/2%:
- Convert 6.5% annual to a monthly rate: 0.065 / 12 = 0.005417
- Calculate the number of months: 25 * 12 = 300
- Substitute into the formula and calculate 'M'
Repeat the same steps for the 8% interest rate:
- Convert 8% annual to a monthly rate: 0.08 / 12 = 0.006667
- Use the same number of months: 300
- Substitute into the formula and calculate 'M'
After calculating 'M' for both rates, subtract the lower monthly payment from the higher one to find the difference.