Question

suppose you obtain a 30-year annuity mortgage of $329000 that you pay for in monthly installments at a quoted yearly rate of 7.5 per cent. what will your loan balance be at the end of the first 15 years of monthly payments?

The answer must be $248,153.73. But how do you calculate this?

Answer 1

First we need to find the monthly payment with PMT function in EXCEL

=PMT(rate,nper,pv,fv,type)

rate=7.5%/12=0.625%

nper=30 years*12=360 months

pv=loan amount=329000

fv=0

=PMT(0.625%,360,-329000,0,0)=$2300.42

The monthly payments=$2300.42

Now we have to find the loan outstanding after 15 years. Use PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

rate=0.625%

nper=15 years*12=180

pmt=monthly payment=2300.42

fv=0

=PV(0.625%,180,2300.42,0,0)=$248,153.73

The loan outstanding after 15 years=$248,153.73