Suppose a 60,000 martgage is to be amortized at 7.5% interest. Find the total amount of interest that would be paid for each term a) 10 years b) 30 years.
To find the total interest paid over a mortgage term, we need to use the formula for calculating an amortization table. The formula takes into account the loan amount, interest rate, and loan term.
The formula for calculating the monthly mortgage payment (PMT) is:
PMT = P[r(1 + r)^n] / [(1 + r)^n - 1]
where:
P = principal amount (loan amount)
r = monthly interest rate (annual interest rate divided by 12)
n = total number of payments (number of years multiplied by 12)
Let's start with part a) finding the total amount of interest paid over 10 years:
Step 1: Convert the annual interest rate to a monthly rate.
Monthly interest rate (r) = Annual interest rate / 12 = 7.5% / 12 = 0.625%
Step 2: Calculate the total number of payments.
Total number of payments (n) = Number of years * 12 = 10 * 12 = 120
Step 3: Calculate the monthly mortgage payment (PMT).
PMT = $60,000 * [0.00625(1 + 0.00625)^120] / [(1 + 0.00625)^120 - 1]
Using a calculator or spreadsheet, solve for PMT to find the monthly payment.
Step 4: Calculate the total interest paid.
Total interest paid = (PMT * Total number of payments) - Principal amount
Repeat the above steps for part b) with a loan term of 30 years.
By following these steps and using the formula, you can find the total interest paid for different mortgage terms.