Suppose you take out a mortgage for $750000 at 5% interest per year compounded annually. If your mortgage is amortized over 5 years, what is your monthly mortgage payment? How much interest will you pay the lender by the end of the mortgage?
To find the monthly mortgage payment, we first need to determine the number of payments you'll make over the life of the loan. This is done by multiplying the number of years the mortgage is amortized by the number of payments made per year (in this case, 12, since payments are made monthly).
Number of payments = 5 years * 12 payments per year = 60 payments.
Now we'll use the mortgage payment formula:
M = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
M = monthly mortgage payment
P = loan principal ($750,000)
r = monthly interest rate (which is the annual interest rate divided by the number of payments per year)
n = total number of payments
First, we'll find the monthly interest rate:
Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.00416667
Now we can plug the variables into the payment formula:
M = $750,000 * (0.00416667(1+0.00416667)^60) / ((1+0.00416667)^60 - 1)
M = $750,000 * (0.00416667(1.00416667)^60) / ((1.00416667)^60 - 1)
M = $750,000 * (0.00416667*1.2830461) / (1.2830461 - 1)
M = $750,000 * (0.00534534) / (0.2830461)
M = $14262.04
So the monthly mortgage payment is about $14,262.04.
Now, let's find the total paid over the life of the loan:
Total paid = Monthly payment * Number of payments
Total paid = $14,262.04 * 60 = $855,722.4
Now, we find the total interest paid by subtracting the loan principal from the total paid:
Interest paid = Total paid - Loan principal
Interest paid = $855,722.4 - $750,000 = $105,722.4
So you will pay $105,722.4 in interest to the lender by the end of the mortgage.