A couple buy a house and take out a 10 year, $60,000 mortgage at j12=9%. They are paying an EMI of $760.05 on it. After three years they sell off the house and pay off the mortgage. They find that in addition to repaying the loan balance they must pay a penalty equal to three times one month interest on the outstanding balance. What total amount must they pay? *

$45 133.65

$49 520.56

$43 233.45

$48 303.32

It is important to note that J12 means that the interest is compounded monthly since there are 12 months in a year.

Monthly interest rate=9%/12= 0.75%

The balance of the loan after three years is the present value of monthly payments for 7 years as computed below:

PV=monthly payment*(1-(1+r)^-n/r

monthly payment=$760.05

r=monthly interest rate= 0.75%

n=number of months in 7 years=12*7=84

PV=$760.05*(1-(1+0.75%)^-84/0.75%

PV=$760.05*(1-(1.0075)^-84/0.0075

PV=$760.05*(1-0.533845266)/0.0075

PV=$760.05*0.466154734/0.0075

PV= $47,240.12 

One month interest on outstanding balance after 3 years= $47,240.12*0.75%=$354.30 

Total payment=$47,240.12+($354.30*3)=$48,303.02(closest to $48 303.32)