Question

7. You need a 25-year, fixed-rate mortgage to buy a new home for $210,000. Your mortgage bank will lend you the money at a 8.1 percent APR for this 300-month loan. However, you can afford monthly payments of only $900, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.

Required: How large will this balloon payment have to be for you to keep your monthly payments at $900?

Answer 1

Amount of the loan = 210000

APR = 8.1%

Monthly payment = 900

First. we need to calculate the remaining Principal to be paid. For this we will use the formula for PV of ordinary annuity.

PV of ordinary annuity = R * 1- (1+i)^-n/ i or R * 1- (1/ (1 +i)ⁿ / i

Remaining Principal = 210000 - 900 * (1- (1/ (1+0.081/12)^25*12 / (0.081 /12))

= 210000 - 900 * 128.46

= 210000 - 115614

= 94386

Now, computation of the Ballon payment:

Ballon payment = 94386 * (1+0.081/12)^25*12

= 94386 * 7.5247

= 710226.33