APY vs APR Explained: How Compounding Quietly Doubles Your Money (or Your Loan Cost)
Blog › Finance · 9 min read · Published 2026-05-07
Understand the real difference between APR and APY, how compounding frequency changes outcomes, and how to compare savings and loans correctly.
Why Two Numbers for the Same Rate?
Banks legally must quote APR on loans and may quote APY on deposits. The reason: APY makes savings yields look bigger and APR makes loans look cheaper, because compounding adds invisible interest you only see when you compute the effective annual rate. The APY Calculator converts between them in one step.
The Math Behind Compounding
The formula is APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. Daily compounding (n=365) on a 5% APR produces 5.127% APY. Monthly compounding produces 5.116%. Continuous compounding — the mathematical limit — produces 5.127%, essentially identical to daily for any rate under 20%.
Why It Matters for Savings
On a $10,000 deposit, the difference between 5.00% APR (annual compounding) and 5.13% APY (daily compounding) is $13 in year one — small. Over 30 years with reinvestment, that gap compounds to over $1,200. Always compare APY to APY across savings accounts.
Why It Matters for Loans
On loans, the same trick works in reverse. A credit card quoted at 18% APR with daily compounding has an effective rate of 19.72% if you carry a balance all year. The bank legally discloses 18%; you actually pay 19.72%.
Continuous Compounding
Continuous compounding uses APY = e^APR − 1. It is the theoretical maximum and the basis for Black-Scholes options pricing and physics decay equations. In real banking, daily compounding is within 0.001% of continuous and is what most US banks use.
Common Mistakes
- Comparing one bank's APR to another's APY (always normalise to APY).
- Ignoring fees — a 5.10% APY with a $5/month fee on $1,000 is actually negative.
- Forgetting that introductory APYs expire — read the post-promo rate.
How to Use the Calculator
Enter your stated APR, choose the compounding frequency, and the calculator returns APY plus the future value over any holding period. Compare two banks side by side and let the math, not the marketing, choose for you.
Bottom Line
APY is the only fair way to compare savings products. APR is the only fair way to compare loan costs before fees. Anyone selling you something will quote whichever number sounds best — your job is to convert.