$50 The bank is ofo ng you a 30-year mortgage that requires annual payments and
ID: 2819276 • Letter: #
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$50 The bank is ofo ng you a 30-year mortgage that requires annual payments and has an interest ate of9% per year. You can afford to pay only S27, 740 per bank agroos to allow you to pay this amount each yoar, yet still borrow $300,000, At the end of the mortgage Iin 30 years) you must make a balloon payment on the Hint The balloon payment will be in addition to the 30th payment The balloon payment is (Round to the nearest dollar.) Enter your answer in the answer box. Save for Later 19 MacBook AirExplanation / Answer
He borrows $300,000 from the bank. We are required to find the leftover portion of the loan which the annual payments of $ 27,740 could not payoff.
We can think of the payments as two different streams. We can find the Future value (FV) of $ 300,000 @9% per year for 30 years in one part . This is the amount of money which is due from us. But we are paying $ 27,740 per year also. Think of it as a deposit @9% per year for 30 year in the bank.
30 years hence, we are due for FV of $ 300,000 but we have deposited an annuity of $ 27,740 also. The balloon payment will be the difference of these two amounts
Balloon payment = FVIF(9%, 30) x - FVIFA (9%, 30) 27,740
= 13.2677 x 300,000 - 136.3075 x 27,740 = 3,980,310 - 3,781,170.05 = $ 199,139.95
So the balloon payment after 30 years will be $199,139.95
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