You need a 35-year, fixed-rate mortgage to buy a new home for $310,000. Your mor
ID: 2384234 • Letter: Y
Question
You need a 35-year, fixed-rate mortgage to buy a new home for $310,000. Your mortgage bank will lend you the money at an APR of 6.05 percent for this 420-month loan. However, you can afford monthly payments of only $1,500, 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 $1,500? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
You need a 35-year, fixed-rate mortgage to buy a new home for $310,000. Your mortgage bank will lend you the money at an APR of 6.05 percent for this 420-month loan. However, you can afford monthly payments of only $1,500, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.
Explanation / Answer
Present value of the $1,500 monthly payments is PMT $1,500 Annual Rate 6.05% Number of period(NPER) 420 Present value Annuity (PVA)(calculated in excel using PV function) $261,528.41 PVA = $1,500[(1 – {1 / [1 + (.0605/12)]^420}) / (.0605/12)] $261,528.41 Cost of Home $310,000 Amount of principal still owe = $310,000 - $261,528.41 $48,471.59 Balloon payment in 35 years, which is the FV of the remaining principal = Present Value $48,471.59 Annual Rate 6.05% Number of period(NPER) 420 Future Value (calculated in excel using FV function) $400,677.90 Balloon payment = $48,471.59[1 + (.0605/12)]420 $400,677.90
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