You need a 30-year, fixed-rate mortgage to buy a new home for $230,000. Your mortgage bank will lend you the money at a 7.6 percent APR for this 360-month loan. However, you can afford monthly payments of only $800, 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
$800? |
Multiple Choice
A) $93,071.12
B) $1,178,050.9
C) $116,697.55
D) $1,132,741.25
E) $1,098,759.01
D) $1,132,741.25
The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $800 monthly payments is:
PVA = $800[(1 – {1 / [1 + (0.076/12)]}^{360}) / (0.076/12)] = $113,302.45
The monthly payments of $800 will amount to a principal payment of $113,302.45. The amount of principal you will still owe is:
$230,000 – $113,302.45 = $116,697.55
This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be:
Balloon payment = $116,697.55[1 + (0.076/12)]^{360} = $1,132,741.25
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