# Optimizing interest for a set of debt payments

Suppose I've got $n$ debts with principals $P_1, P_2, ..., P_n$, with corresponding interest rates $r_1, r_2, ..., r_n$, compounded monthly.

Further, assume I have a constant $A$ dollars per month to split between all $n$ debt payments.

EDIT: There are monthly minimum interest payments as well.

Given these constraints, how can I minimize the total interest paid?

• Say I have debts with principals of \$10 and \$2, with rates 10% and 20%, respectively. I must pay at least the interest on each, each pay period. In addition, I have an extra dollar to spend each month. Then, your claim is that I should simply pay the one with the 50% rate first? – Zduff Sep 24 '19 at 20:49