Question

If you are considering a 30-year loan paid monthly and the interest rate on the loan of $145,000 is at 4.25%, how many months could you shave off of the loan by paying an extra $200 per month ?

            A) About 33 months, or just less than 3 years

            B) About 83 months, or about 7 years

            C) About 126 months or about 10 and a half years

            D) About 79 months, or just less than 7 years

Answer 1

Monthly loan payment is calculated using PMT function in Excel :

rate = 4.25% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 145000 (loan amount)

PMT is calculated to be $713.31

If an extra $200 is paid per month, monthly payment = $713.31 + $200 = $913.31

The number of months to pay off the loan is calculated using NPER function in Excel :

rate = 4.25% / 12   (converting annual rate into monthly rate)

pmt = -913.31 (Monthly payment. This is entered with a negative sign because it is a payment)

pv = 145000 (loan amount)

NPER is calculated to be 234

Original loan term = 30 * 12 = 360 months

However the loan is paid off in 234 months

Months reduced by paying higher monthly payment = 360 - 234 = 126 months

The answer is C