Question

Professor Elmtwig makes a monthly payment of $1600 on his mortgage. The original term of the mortgage is for 35 years at 8.75% interest compounded semi-annually. His lender suggests that if he makes bi-weekly payments of $800, it will reduce how long it will take to pay off the mortgage. How much did Professor Elmtwig originally borrow? (Round to the nearest cent, do not use dollar signs)

Answer 1

Number of months =35*12 =420
Effective monthly rate =(1+8.75%/2)^(1/6)-1 =0.716219288838582%
PV of mortgage or amount originally borrowed=PMT*(1-(1+r)^-n)/r) =1600*(1-(1+0.716219288838582%)^-420)/0.716219288838582%)=212,244.1150 or 212,244.12

Effective biweekly rate =(1+8.75%/2)^(1/13)-1 =0.32992766086386%
PMT=800
Number of Periods using Financial Calculator
I/Y =0.32992766086386%;PMT=800;PV=-212,244.1150;CPT N =632.0773 biweeks or 24.31 years

It will reduce number of years by =35-24.31 =10.69 years