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Mike bayles has just arranged to purchase a $400,000 vacation home in the bahamas with a 20 percent down payment.the mortgage has an 8 percent stated annual interest rate, compounded monthly, and calls for equal monthly payments over the next 30 years. his first payment will be due one month from now. however, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of year 8.there were no other transaction costs or finance charges. how much will mike's balloon payment be in eight years?

Respuesta :

mathmate
Given:
Loan=400000-downpayment=400000(1-0.2)=320,000
i=interest rate = 8% nominal = 0.08/12 per month
term=30 years => n=30*12=360

Question: what the the balloon payment at the end of the eighth year to pay off the mortgage.


Solution:
Monthly payment
[tex]A=\frac{P(i*(1+i)^{n})}{(1+i)^{n}-1}[/tex]
[tex]=\frac{320000((0.08/12)*(1+0.08/12)^{360})}{(1+0.08/12)^{360}-1}[/tex]
=2348.0466 per month

At the end of the eighth year, 
Future value of the loan
F1=320000(1+0.08/12)^(8*12)
=605586.310
Future value of payments
[tex]F2=\frac{A((1+i)^{n}-1)}{i}[/tex]
[tex]=\frac{2348.0466((1+0.08/12)^{8*12}-1)}{0.08/12}[/tex]
=314329.676

Therefore the balloon payment to pay off mortgage
=F1-F2
=605586.310-314329.676
=291256.63  (to the nearest cent)

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