Some Nontrivial Properties of a Formula for Compound Interest

TL;DR

This paper investigates the mathematical properties of a classical compound interest formula, revealing that the outstanding balance function can exhibit non-monotonic curvature behavior with respect to the interest rate.

Contribution

It provides a detailed analysis showing that the outstanding balance function is not always concave, challenging common assumptions in financial modeling.

Findings

Outstanding balance function can be initially convex and then concave in interest rate

The classical model's functions exhibit complex curvature properties

Implications for financial decision-making and interest rate sensitivity

Abstract

We analyze the classical model of compound interest with a constant per-period payment and interest rate. We examine the outstanding balance function as well as the periodic payment function and show that the outstanding balance function is not generally concave in the interest rate, but instead may be initially convex on its domain and then concave.