Question

you have purchased a condo and are financing a mortgage of $200,000 over 20-years with monthly payments. Your mortgage rate is quoted as APR 7.25% compounded semi annually. After 5 years you make a lump sum payment of $50,000 towards your mortgage principal and continue with your regular payments. By approx how many years will it reduce the amount of time take to pay off the mortgage?

Answer 1

Since frequency of compounding (m = 2) and frequency of payment (n = 12) are different, we need to calculate the effective rate per payment period.

rate per month = [(1 + APR/m)^(m/n)] -1 = [(1 + 7.25%/2)^(2/12)] -1 = 0.5952%

Calculation of monthly payment:

PV (mortgage amount) = 200,000; N (number of payments) = 20*12 = 240; rate = 0.5952%, solve for PMT.

Monthly payment = 1,567.79

Outstanding balance after 5 years:

PV = 200,000; PMT = -1,567.79; N = 5*12 = 60; rate = 0.5952%, solve for FV

Outstanding balance =172,886.59

Net balance remaining after payment of lump sum = 172,886.59 - 50,000 = 122,886.59

Calculation of number of payments, it will take to pay off the net balance at the same monthly payment:

PV = 122,886.59; PMT = -1,567.79; rate = 0.5952%, solve for NPER.

Number of payments = 105.89

Number of years = 105.89/12 = 8.82 years

Reduction in time = original duration of the mortgage - 5 - 8.82 = 20 - 5 - 8.82 = 6.18 years (Answer)