Final Payment

Study guide: Exam FM-2

The final payment on a loan is the last payment made to retire the outstanding balance, which may differ from the regular payment amount when the Term of Loan is not an integer number of periods.

• There are two conventions:
  • Drop Payment: the remainder is paid one period after the last regular payment, so the final payment is smaller than the regular payment
  • Balloon Payment: the remainder is added to the last regular payment, so the final payment is larger than the regular payment
• The final payment amount equals the Outstanding Balance at the previous payment date accumulated by one period.

Computing the Drop Payment A 1{,}000 loan at 6\% annual interest is repaid with annual payments of 250 for as long as necessary, plus a smaller final payment one year after the last full payment. Find the term of the loan and the drop payment.

Answer Solve 1000 = 250\,a_{\overline{n}|6\%}, so a_{\overline{n}|} = 4:

\begin{align*}
n &= \frac{-\ln(1 - 0.06 \times 4)}{\ln 1.06} \\
&= \frac{0.274437}{0.058269} \\
&= 4.71
\end{align*}

So 4 full payments are made. The balance just after the 4th, retrospectively, with (1.06)^4 = 1.262477 and s_{\overline{4}|6\%} = 4.374616:

\begin{align*}
B_4 &= 1000(1.06)^4 - 250\,s_{\overline{4}|6\%} \\
&= 1262.477 - 1093.654 \\
&= 168.823
\end{align*}

The drop payment at the end of year 5 is 168.823(1.06) = 178.95, smaller than the regular 250.