Aaron Grider buys a home for $120500. After a 15% downpayment, the rest is financed at 8% interest for 9 years. What equal quarterly payments will be required to amortize this mortgage loan?
What is the total amount of interest Aaron will pay on the loan?
I subtracted the 15% down payment from the total purchase price.
$120500.00-$18075.00=$102425.00 which becomes the purchase amount I now work with. So, I work the original problem using $102425.00 at 8% for 9 years. Yes, No?
Yes, you have correctly subtracted the down payment amount from the total purchase price, and now you should work with the remaining amount of $102,425.00.
To calculate the equal quarterly payments required to amortize the mortgage loan, you can use the formula for the loan payment amount:
PMT = (PV * r) / (1 - (1 + r)^(-n))
Where:
PMT = the equal quarterly payment
PV = the present value of the loan (the remaining amount after the down payment)
r = the quarterly interest rate (8% divided by 4, or 0.08/4)
n = the total number of quarters (9 years * 4 quarters per year, or 36 quarters)
Plugging in the values:
PV = $102,425.00
r = 0.08/4 = 0.02 (2%)
n = 36
PMT = (102425 * 0.02) / (1 - (1 + 0.02)^(-36))
Calculating this expression will give you the equal quarterly payment required to amortize the mortgage loan.
To find the total amount of interest Aaron will pay on the loan, you can multiply the quarterly payment amount by the total number of quarters (36) and then subtract the principal loan amount (PV).
Total interest = (PMT * n) - PV
Calculating this expression will give you the total amount of interest Aaron will pay on the loan.