Question

You need a 30-year, fixed-rate mortgage to buy a new home for $280,000. Your mortgage bank will lend you the money at an APR of 5.75 percent for this 360-month loan. However, you can afford monthly payments of only $1,200, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $1,200

Answer 1

Answer: $‭415,688‬

Step-by-step explanation:

First find the future value of paying $1,200 every month for 360 months.

This is the future value of an annuity:

= Payment * ([1 + interest) ^ no. of periods - 1) / interest

Use periodic interest = 5.75%/ 12

30 years * 12 = 360

= 1,200 * ( ( 1 + 5.75%/12)³⁶⁰ - 1) / 5.75% / 12

= $1,149,357.14

Future value of the loan amount is:

= 280,000 * (1 + 5.75% / 12) ³⁶⁰

= $1,565,045.14

Ballon Payment = 1,565,045.14 - 1,149,357.14

= $‭415,688‬