A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year amortization. What this means is that the borrower makes a payment every month of a fixed amount

Question

A common arrangement in real estate lending might call for a 5-year loan with, say, a 15-year amortization. What this means is that the borrower makes a payment every month of a fixed amount based on a 15-year amortization. However, after 60 months, the borrower makes a single, much larger payment called a “balloon” or “bullet” to pay off the loan. Because the monthly payments don’t fully pay off the loan, the loan is said to be partially amortized.
Suppose we have a $100,000 commercial mortgage with a 12 percent APR and a 20- year (240-month) amortization. Further suppose the mortgage has a five-year balloon.
What will the monthly payment be? How big will the balloon payment be?

Accepted Answer

The monthly payment can be calculated based on an ordinary annuity with a present value of $100,000. There are 240 payments, and the interest rate is 1 percent per month.
The payment is:

$100, 000=[latex]C×{[1-(1/1.01^{240})]/.01}[/latex]

=C×90.8194

C=$1,101. 09

Now, there is an easy way and a hard way to determine the balloon payment. The hard way is to actually amortize the loan for 60 months to see what the balance is at that time. The easy way is to recognize that after 60 months, we have a 240 60 180-month loan. The payment is still $1,101.09 per month, and the interest rate is still 1 percent per month. The loan balance is thus the present value of the remaining payments:

Loan balance=$[latex]1,101. 09×{[1-(1/1.01^{180})]/.01}[/latex]

=$1,101. 09×83.3217

=$91,744.69

The balloon payment is a substantial $91,744. Why is it so large? To get an idea, consider the first payment on the mortgage. The interest in the first month is $100,000×.01=$1,000.
Your payment is $1,101.09, so the loan balance declines by only $101.09. Because the loan balance declines so slowly, the cumulative “pay down” over five years is not great.

Question 6.13: A common arrangement in real estate lending might call for a...

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