pplpod30 Des 2025

Demystifying APY: Compounding Interest and the Truth in Savings

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In this episode, we break down the Annual Percentage Yield (APY), a normalized representation of an interest rate based on a compounding period of one year. We discuss how APY figures allow for a reasonable, single-point comparison of different financial offerings that use varying compounding schedules, noting that these figures do not account for account fees.

Listeners will learn the critical difference between APY and the Annual Percentage Rate (APR); while APR usually refers to the rate paid by a borrower, APY generally refers to the rate paid to a depositor. Financial institutions often quote APY because it highlights the higher return a customer receives at the end of a term due to compounding.

We also explore the mathematical side of APY, illustrating how the formula $(1 + i_{nom}/N)^N - 1$ demonstrates that as the nominal interest rate increases, the gap between it and the APY widens. Finally, we cover the regulatory landscape in the United States, specifically the Truth in Savings Act of 1991, which mandates how institutions calculate APY based on a $100 deposit over a 365-day period.

Analogy To understand the difference between a simple nominal rate (like APR) and APY, imagine planting a tree. The nominal rate is like measuring how much the tree grows based only on the water you give it once a year. APY, however, measures the tree's growth assuming that every new branch the tree grows (interest) also starts growing its own leaves and branches (compounding) throughout the year. The more often those new branches appear, the fuller the tree looks at the end of the year—that final "fullness" is your APY.

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