You would like to buy a house that costs $350,000. You have $50,000 in cash that

Question

You would like to buy a house that costs $350,000. You have $50,000 in cash that you can put down on the house, but you need to borrow the rest of the purchase price. The bank is offering you a 30-year mortgage that requires annual payments and has an interest rate of 10% per year. You can afford to pay only 30,230 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a balloon payment, that is, you must repay the remaining balance on the mortgage. How much will be this balloon payment? Hint. The balloon payment will be in addition to the 30th payment to The balloon payment is (Round to the nearest dollar) (Round to30th ament n the mongage su o 30 n intae entis s

Explanation / Answer

Cost of the house is $350,000. Out of which we are paying off $50,000 by cash at the beginning itself. So, we are taking a loan for $300,000 which is a 30-year mortgage loan.

If $30,230 is paid every year for 30 years, the present value of all these payments at the beginning = P

P = PMT x ((1 - (1 / (1 + r) ^ n)) / r)

Where:

P = the present value of an annuity stream = ?

PMT = the dollar amount of each annuity payment = $ 30,230

r = the interest rate (also known as the discount rate) = 10%

n = the number of periods in which payments will be made = 30

Therefore P= 30230(1-(1/(1+0.1))30)/0.1

P = $284,975.62.

Thus, all the cash flows when discounted to year 0 had accounted for only  $259,068.75. Whereas, we need to pay back $300,000 loan.

Thus value of balloon payment at year 0 = $300,000-  $284,975.62 = $15,024.38

But Balloon payment is done at the end of year 30 as an additional payment to repay off the balance.

Thus the value of balloon payment at Year 30 = $15,024.38*(1+0.1)^30 = $262,166

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