Question

I know for this problem we first have to find the payment (PMT) then we are suppose to subtract the years from the initial years ( 30 years - the years that have gone by= new number of years) then we can find the Future Value. But I am still not sure if I am understanding the problem correctly.

"13 years ago you borrowed $112564 to buy a new house. The interest rate quoted to you was 7.22 percent for 30 years with monthly payments. Assuming you have made regular monthly payments up to now, what is the amount (in$) you still owe on the loan today?"

Answer 1

Amount borrowed = $112,564
Period of loan = 30 years or 360 months
Annual interest rate = 7.22%
Monthly interest rate = 0.6017%

Let monthly payment be $x

$112,564 = $x/1.006017 + $x/1.006017^2 + ... + $x/1.006017^359 + $x/1.006017^360
$112,564 = $x * (1 - (1/1.006017)^360) / 0.006017
$112,564 = $x * 147.022123
$x = $765.63

Monthly payment = $765.63

Remaining period of loan = 17 years or 204 months

Loan remaining = $765.63/1.006017 + $765.63/1.006017^2 + ... + $765.63/1.006017^203 + $765.63/1.006017^204
Loan remaining = $765.63 * (1 - (1/1.006017)^204) / 0.006017
Loan remaining = $765.63 * 117.315375
Loan remaining = $89,820.17

So, you still owe $89,820.17 on the loan today.