Question

A family took a 20 year mortgage of $195,000 at 5.75% per year
compounded monthly. Immediately after the 85^{th} monthly
payment, they decided to re-finance this mortgage because they
found a lower rate of 3.75% per year compounded monthly. If they
continue the same amount of monthly payments as before, how long
will it take to pay off this mortgage?

Answer #1

First find the monthly payment using interest rate of 5.75%/12 = 0.47917% per month. The time is 20*12 = 240 months and monthly payment is 195000(A/P, 0.47917%, 240) = 1369.06.

Now after 85th payment, the balance is 1369.96(P/A, 0.47917%, 240 – 85) = 149524.72. This amount is refinanced at 3.75%/12 = 0.3125% per month. Find the number of payments using NPER(0.3125%,1369.06,-149524.72) = 134 months.

Thus, it would take 134 more months to payoff the mortgage.

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