Question

you need a 20-year, fixed-rate mortgage to buy a new home for $210,000. Your mortgage bank will lend you the money at a 7.1 percent APR for this 240 month loan. However, you can afford monthly payments of $1,000, so you offer to pay off any remaining balance at the end of the loan in the form of a single balloon payment. HOw large will this balloon payment have ot be for you to keep your monthly payments at $1000

Answer 1

Answer: $337,869.73

Explanation:

Find out the future value of $1,000 given an interest rate of 7.1%. If this amount is less than the future value of $210,000, the difference is added to the final payment to come up with the balloon payment.

The APR needs to be made periodic:

= 7.1% / 12

The $1,000 payment is an annuity so this can be calculated as:

= Annuity * ( ( 1 + rate) ^ number of periods - 1) / rate

= 1,000 * ( ( 1 + 7.1/ 12%) ²⁴⁰ - 1) / 7.1/12%

= $527,297.83

Future value of $210,000

= 210,000 * ( 1 + 7.1/ 12%) ²⁴⁰

= $865,167.56

Balloon payment will be:

= 865,167.56 - 527,297.83

= $337,869.73