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 a​ 30-year mortgage that requires annual payments and has an interest rate of 7 % per year. You can afford to pay only $ 22,970 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 this balloon payment​ be?

Answer 1

House Cost = $ 350000 and Down Payment = $ 50000  

Borrowing = $ 300000 and Rate of Interest = 7 %

Annual Payment Possible = $ 22970 and Payment Tenure = 30 years

Now the annual payment of $ 22970 will be able to payoff the total loan in say some N years where N> 30. However, the loan is only for 30 years followed by a balloon payment of the remaining principal. If an amortizing loan is paid up/interrupted in the middle of its tenure, then the principal outstanding at the point of interruption is equal to the total present value of its remaining periodic repayments at the point of interruption. In this context, the point of interruption is 30 years and periodic repayments are $ 22970.

Now , 300000 = 22970 x (1/0.07) x [1-{1/(1.07)^(N)}]

Using trial and error/ EXCEL's Goal Seek Function to determine the value of N , we get:

N ~ 37.6 years

Therefore, Principal Outstanding = Balloon Payment = PV of Remaining Periodic Repayments at 30 years = 22970 x (1/0.07) x [1-{1/(1.07)^(37.6 - 30)}] = $ 113912.3 Approximately.