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You need a 30-year, fixed-rate mortgage to buy a new home for $225,000. your bank will lend you the money at an apr of 5.5 percent with monthly compounding. you can only afford monthly payments of $1,000 for principal and interest, so you offer to pay off any remaining loan balance at the end of the loan term in the form of a single balloon payment. what will be the amount of the balloon payment?

Respuesta :

mathmate
Loan amount, P = 225000
interest = 5.5%/12  per month
Monthly payment, A = 1000

At the end of 30 years, 
Future value of loan (with zero repayment)
F1=225000*(1+.055/12)^(30*12)
=1167162.264

Future value of repayment, A=1000 per month
F2=[tex]\frac{A((1+i)^n-1)}{i}[/tex]
=[tex]\frac{1000((1+.055/12)^{360}-1)}{.055/12}[/tex]
=913611.893

Therefore balloon payment
= F1-F2
=1167162.264-913611.893
=253550.37   (to the nearest cent)

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