Track 1 · Foundations → Phase 6: Interest & Compounding — The Engine
APR vs. APY — why the same "rate" isn't the same number ⚙
APR is the rate before compounding is folded in; APY is the rate after — the honest number — which is why a 5% APR compounded monthly actually works out to 5.12% APY.
The situation
You’re comparing two savings accounts. One brags about a “5% rate,” the other advertises a “5.1% APY.” A card offer quotes a “24.99% APR.” Three numbers, three different little acronyms, and a nagging feeling that they’re not quite measuring the same thing. They’re not — and once you know which is which, you can compare any two offers honestly instead of guessing.
The idea
Both APR and APY describe a yearly rate. The difference is whether compounding is baked in.
- APR — Annual Percentage Rate. The rate before compounding is folded in. It’s the headline number you’ll usually see on borrowing — credit cards, loans. Think of it as the raw yearly rate.
- APY — Annual Percentage Yield. The rate after compounding is folded in. It’s the number you’ll usually see on savings, and it reflects what you actually earn once interest starts earning interest across the year. APY is the honest number.
Why are they different at all? Because of the snowball you just saw. If a 5% rate compounds monthly, you earn a little interest on your interest each month — so by the end of the year you’ve actually earned slightly more than a flat 5%. APY captures that “slightly more.” The more often it compounds, the bigger the gap between the stated rate and the true yield.
The rule of thumb: on savings, compare by APY — it already includes compounding. On debt, the APR is the headline, but your real cost runs a touch higher than the stated APR for the very same reason. (That second half threads straight into the next lesson, where the same engine becomes the enemy.)
By the numbers
Take the cleanest case: a 5% rate, compounded monthly. What’s the true yearly yield?
Each month earns one-twelfth of 5%, but because each month’s interest joins the balance and then earns interest itself, the twelve months stack up to a little more than 5%:
| Same 5% rate, compounded… | Works out to (APY) |
|---|---|
| Once a year | 5.00% |
| Monthly | 5.12% |
| Daily | about 5.13% |
That’s the headline: 5% APR compounded monthly = 5.12% APY. Not a huge gap on a small balance for one year — but it’s the honest comparison number, and on big balances over many years it adds up exactly the way the snowball does. Notice, too, that compounding daily nudges it a hair higher still (about 5.13%): same nominal rate, more frequent compounding, slightly bigger yield.
The calculator below starts on this exact case — 5% APR, monthly, showing 5.12% APY. Change the rate or the compounding frequency and watch the APY shift. Flip it to daily and see it tick up; flip it to yearly and watch it collapse back to the plain rate. Same rate, different honest number — that’s the entire idea, live.
Where this fits
APR and APY aren’t bank tricks; they’re just two honest ways to quote the same engine — one before compounding, one after. On savings you hunt for the highest APY. On debt you respect the APR and remember the real cost is a bit steeper. Keep both straight and no rate label can fool you. Next: the two faces of this engine — the same compounding that grows your savings is what makes debt so hard to escape.
SAME RATE, TWO NUMBERS
5% APR 5.12% APY
APR is the rate before compounding is folded in. APY is the rate after — and it's the honest number. The more often interest compounds, the bigger the gap between the two.
Do it
Find a rate on one of your accounts and check the label: does it say APR or APY? On savings you want to compare by APY; on a card, the APR is your cost. Knowing which one you're looking at is half the battle.
Check yourself
1. What's the difference between APR and APY?
APR is the stated annual rate before you account for compounding within the year. APY rolls the compounding in, so it reflects what you actually earn (or, on the cost side, what it effectively works out to). APY is the more honest number.
2. A savings account advertises a 5% rate compounded monthly. What's the APY?
Compounding monthly means you earn a little interest on your interest each month, so the effective yearly yield is slightly above 5% — about 5.12% APY. That's the number the calculator below shows.
3. Why does the same 5% rate become a bigger APY when it compounds more often?
The more often interest is added, the sooner it starts earning its own interest. So 5% compounded daily yields a touch more than 5% compounded monthly, which yields more than 5% compounded once a year. Same nominal rate, different APY.
4. When comparing two savings accounts, which number should you compare?
APY is the apples-to-apples number for savings: it bakes in the compounding, so a higher APY genuinely means more money. Comparing raw rates with different compounding can mislead you.
Keep this
APR is the rate before compounding; APY is the rate after compounding is folded in. 5% APR compounded monthly = 5.12% APY. On savings, compare by APY (the honest number); on debt, your real cost runs a bit above the stated APR for the same reason.