Drop Payment

Study guide: Exam FM-2

A drop payment is a final loan payment that is smaller than the regular payment, made one period after the last regular payment — on the date the next regular payment would have fallen. It arises when level payments continue for as long as necessary and the Term of Loan is not a whole number of periods: the drop payment retires the remaining Outstanding Balance.

If regular payments are $P$ at rate $i$ per period, $n$ is the number of full payments (the integer part of the term), and $B_n$ is the outstanding balance just after the $n$ -th payment, the drop payment one period later is:

$\text{Drop Payment} = B_n(1+i)$

It is smaller than $P$ when $B_n(1+i) < P$ , that is $B_n < P\,v$ . That is why $n$ counts only full payments: if $B_n(1+i) \geq P$ , another full payment could still be made.
This contrasts with a Balloon Payment, which is larger than the regular payment: the same remainder is added to the last regular payment instead of being paid a period later.

Identifying and Computing a Drop Payment A loan is repaid with annual payments of $500$ . After 6 full payments the outstanding balance is $450$ . Find the drop payment at the end of year 7 at $i = 5\%$ .

Answer Since $450 < 500/1.05 = 476.19$ , a seventh full payment cannot be made, and the drop payment is $450 \times 1.05 = 472.50$ — less than the regular $500$ payment.