Question

Is there a formula to quickly calculate amortized interest? I know how to do it for each individual payment period (interest= [principle amount]x[interest rate]) and subtracting the amount of the payment that goes towards the principle, and doing it over and over again. However, this process takes too long once you get more payment periods. I am trying to answer the following question:

Q: You have paid for 20 years of your 30 year mortgage and make monthly payments of $2,545. Assuming the APR on the loan is 6.6% per year, compounded monthly, a) how much would you need today to pay off the remaining balance on the mortgage? Based on this information, b) what was the amount of the original mortgage?

So far, I have calculated the original mortgage to be $398,491.33 (is this right? I used the present value of an annuity formula- not sure if this is correct process). I am struggling with part a.

Answer 1

There will be 10 years left on the mortgage i.e., 12*10 payments

Loan left=Present Value of payments=Present Value of ordinary annuity=Annuity/(r)*(1-1/(1+r)^n)=2545/(6.6%/12)*(1-1/(1+6.6%/12)^(12*10))
=223133.1805