Question

A family took a 20 year mortgage of $195,000 at 5.75% per year compounded monthly. Immediately after the 85th monthly payment, they decided to re-finance this mortgage because they found a lower rate of 3.75% per month 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

Borrowed amount = $ 195,000,

Time = 20 years = 240 months

Interest rate = 5.75% per year = (5.75/12)% per month

Calculating the amount paid monthly

The monthly installment = $ 1,369

After 85th payment number of payments yet to be paid is 155 months. Amount after the 85th payment can be calculated as follows

You seek to take a loan on the amount $ 149,525 agar a rate of 3.75% per year. In this case you continue to pay $ 1,369. We have to calculate the number of months in which the amount will be paid off.

New interest rate = 3.75% per year, compounded monthly

You continue paying monthly installment of $ 1,369

Taking log on both sides we get

Number of months to pay off loan = 134 months.

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