You need a 35-year, fixed-rate mortgage to buy a new home for $260,000. Your mortgage bank will lend you the money at an APR of 5.55 percent for this 420-month loan. However, you can afford monthly payments of only $1000. 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 $1:000?

An annual percentage rate (APR) is the annual rate that is paid on amount borrowed or received from an investment. It is usually stated as a percentage which indicates the annual cost of funds over the term of a loan.

From the question we have:

Mortgage loan amount = $260,000

Monthly repayment amount affordable = $1,000

ARR = 5.55%

Monthly ARR = 5.55% ÷ 12 = 0.4625%

Mortgage loan tenure in years = 35

Mortgage Loan tenure in months = 35 × 12 = 420

ARR amount payable monthly = Mortgage Loan × Monthly ARR

= $260,000 × 0.4625%

= $1,202.50

Total ARR amount payable = ARR amount payable monthly × Mortgage Loan tenure in months

Total ARR amount payable = $1,202.50 × 420

= $505,050.00

Total mortgage loan to repay after 35 years = Mortgage loan amount + Total ARR amount payable

Total mortgage loan to repay after 420 months = $260,000 + $505,050

= $765,050

Total repayment amount affordable = Monthly repayment amount affordable × Mortgage Loan tenure in months

Total repayment amount affordable = $1,000 × 420

= $420,000

Balloon payment after 420 months = Total mortgage loan to repay after 420 months - Total repayment amount affordable

Balloon payment after 420 months = $765,050 - $420,000

= $345,050

Therefore, the balloon payment have to be as large as $345,050 to keep monthly payments at $1,000.