Loans:What is the interest expense

What is the interest expense in the 200th payment on a 30-year, $100,000 mortgage at 6%?

Solution

You can do this a few ways. Some will make a full amortization table, but you can also do it with a few equations.

First, figure out what the effective interest rate is per payment period. In this case, $( 1+\frac{.06}{12} )^1 -1 = .005$. The convention in the US is that mortgages are paid monthly, and that the interest compounds monthly.

Second, calculate the payments for this loan, $100000(A|P,i=.005,360) = 599.55$.

Next, find the balance remaining after you made 199 payments, you will use this to find the interest expense in the next period. You are basically finding one line of the amortization table. This is $599.55 (P|A, i=.005, 360-199)= 66192.05$.

Finally, to find the interest expense on the next payment just multiply the effective interest rate per payment period by the balance remaining, $.005 (66192.05) = 330.96$

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