Suppose you obtain a mortgage loan of $215,000 at an annual interest rate of 7%. How much less is the interest paid over the life of a 20 year loan than over the life of a 25 year loan round your answer to the nearest cent
To calculate the difference in interest paid over the life of a 20-year loan compared to a 25-year loan, you'll need to calculate the total interest paid for each loan term.
First, let's find the interest paid for the 20-year loan:
Loan amount: $215,000
Annual interest rate: 7%
Loan term: 20 years
To calculate the interest paid, you can use the formula for calculating the monthly payment for a mortgage loan:
Monthly interest rate = (annual interest rate / 100) / 12 = (7 / 100) / 12 = 0.00583
Loan term in months = 20 years * 12 months/year = 240 months
Using the formula for calculating the monthly payment, we can calculate the monthly payment amount:
Monthly payment = Loan amount * (Monthly interest rate / (1 - (1 + Monthly interest rate)^(-Loan term in months)))
Monthly payment = $215,000 * (0.00583 / (1 - (1 + 0.00583)^(-240)))
Monthly payment ≈ $1,593.64
The total interest paid for a 20-year loan can be calculated by subtracting the loan amount from the total amount paid over the loan term:
Total payment = Monthly payment * Loan term in months
Total payment = $1,593.64 * 240 months ≈ $382,473.60
Total interest paid = Total payment - Loan amount
Total interest paid = $382,473.60 - $215,000 = $167,473.60
Now, let's find the interest paid for the 25-year loan:
Loan amount: $215,000
Annual interest rate: 7%
Loan term: 25 years
Using the same calculations as above, we can find the monthly payment:
Monthly interest rate = (7 / 100) / 12 = 0.00583
Loan term in months = 25 years * 12 months/year = 300 months
Monthly payment = $215,000 * (0.00583 / (1 - (1 + 0.00583)^(-300)))
Monthly payment ≈ $1,484.46
Total payment = Monthly payment * Loan term in months
Total payment = $1,484.46 * 300 months ≈ $445,337.82
Total interest paid = Total payment - Loan amount
Total interest paid = $445,337.82 - $215,000 = $230,337.82
To find the difference in interest paid over the life of the loans, subtract the interest paid for the 20-year loan from the interest paid for the 25-year loan:
Difference in interest paid = Interest paid (25-year loan) - Interest paid (20-year loan)
Difference in interest paid = $230,337.82 - $167,473.60 ≈ $62,864.22
So, the difference in interest paid over the life of a 20-year loan compared to a 25-year loan is approximately $62,864.22.