16  Balloon and Drop Payments

When a loan is paid off by a sequence of level payments and a final payment that is not equal to the level payments, the final payment is either a balloon or drop payment.

\[\begin{align}\text{final payment} > P &\implies \text{balloon payment} \\ \text{final payment} < P &\implies \text{drop payment} \end{align}\] If the final payment is made at the end of \(n\) payment periods, then \[\text{final payment} = B_{n-1}\times (1+i)\] Example: A loan of \(\$10,000\) is to be repaid with level annual payments of \(\$1,000\) and a final payment. The annual effective interest rate is \(5\%\). Calculate the final payment if it is:

• a balloon payment
• a drop payment

Solution: We use the BA II calculator to find the term of the loan:

5 [I/Y] 10000 [+/-] [PV] 1000 [PMT] [CPT] [N] -> N = 14.21

If the final payment is a balloon payment, then \(n = 14\). We can find the balance at the end of 13 years, and then accumulate for one more year:

13 [N] [CPT] [FV] [×] 1.05 [=] (1,200.68)

On the other hand, If the final payment is a balloon payment, then \(n = 15\). Similarly, we would have:

14 [N] [CPT] [FV] [×] 1.05 [=] (210.72)