APY vs. APR and the actual math of savings interest

Savings account marketing runs on percentages most people never quite decode: APY here, APR there, 'compounded daily' in the fine print, 'up to' doing heavy lifting in the headline. The math underneath is genuinely simple — simpler than banks' marketing departments would prefer — and knowing it takes about ten minutes. After that, you can price any account, spot the gimmicks, and know exactly what a rate change costs you in dollars.

APR vs. APY: the same rate, before and after compounding

APR (annual percentage rate) is the raw interest rate before compounding. APY (annual percentage yield) is what you actually earn in a year once compounding is included — interest earning interest on itself. Savings accounts advertise APY because it's the bigger, truer number for money you're receiving; loans advertise APR because it's the smaller, gentler number for money you're paying. For comparing savings accounts, APY is the only number you need, and it's directly comparable across banks regardless of how often each one compounds.

The compounding-frequency myth

Banks love advertising 'compounded daily!' as if it were a feature worth switching for. Run the numbers: $10,000 at a 4% APR compounded annually earns $400.00. Compounded monthly: $407.42. Compounded daily: $408.08. The leap from annual to monthly compounding is worth $7.42 a year; from monthly to daily, 66 cents. Meanwhile the difference between a 4.0% APY and a 4.5% APY on the same balance is $50 a year. Compounding frequency is a rounding error dressed up as a selling point — chase the APY, ignore the frequency, and remember APY already bakes the compounding in anyway.

The whole table spans $8.08 — about the cost of a sandwich, per year, on ten grand. Now compare that to the spread between banks: the same $10,000 at a megabank paying 0.01% earns a dollar a year, while a competitive high-yield account at 4.25% earns $425. The frequency column is where marketing happens; the rate itself is where your money happens.

The gap compounds too

Rate differences look modest in year one and embarrassing by year ten, because the interest you earn starts earning. Park $10,000 and add nothing: at 0.01% you have $10,010 after a decade — ten dollars for ten years of loyalty. At 4% APY, the same untouched deposit grows to about $14,802, and the final year's interest ($569) is larger than the first year's ($400) because the balance itself grew. That widening is the entire pitch for moving money once and letting the account do the work.

How interest actually posts to your account

One mechanical detail saves confusion later: most banks accrue interest daily on your balance but post it monthly, usually on the statement date. Daily accrual means the money earns from the day it arrives — moving $5,000 in mid-month still earns roughly half a month of interest on it, so there's no reason to time deposits around statement cycles. It also means the posted amount wobbles month to month: a 31-day month pays about 3% more than a 30-day one, and February shortchanges you slightly. If a month's interest looks off, check the day count and your average balance before assuming the rate changed — then check the rate anyway, because sometimes it did.

Reading the fine print like an adversary

• 'Up to 5.00% APY': the top rate usually applies only to a slice (the first $500, or with direct deposit plus ten debit swipes). Compute the blended rate on YOUR balance before being impressed.
• Teaser rates: ' 5.00% for 6 months, then our standard rate' — which is often under 1%. Price the full year: 5% for half a year plus 0.5% for the other half averages 2.75%.
• Rate tiers that punish size: some accounts pay the headline rate only below a cap, and near-zero above it. Fine for small balances, a trap for your emergency fund.
• Variable means variable: every savings APY can change tomorrow without your consent. Banks raise slowly and cut quickly; check your actual rate twice a year, because 'I opened it at 4.5%' is not the same as 'it pays 4.5%.'
• The federal Truth in Savings Act requires banks to disclose APY, fees, and rate rules before you open the account — the disclosure document is where the 'up to' games go to die.

A worked 'up to' example, because they're everywhere: an account advertises 5.00% APY on the first $1,000 and 0.25% above it. On a $15,000 balance that's $50 on the first slice plus $35 on the remaining $14,000 — $85 a year, a blended 0.57%. The plain 4.25% account pays $637.50 on the same money. The headline number was more than seven times the real one, and the only tool needed to catch it was one minute of multiplication.

Two mental shortcuts worth keeping

The Rule of 72 estimates doubling time: divide 72 by the rate. At 4%, money doubles in about 18 years; at 0.01%, in about 7,200 years — a genuinely useful way to feel the difference between account choices. And for any advertised rate, the honest question is always the dollar version: 'on my balance, that's how much per year?' Percentages are abstract by design; $637 versus $1.50 is not.

The bottom line

APY is the real number, APR is the raw ingredient, and compounding frequency is a distraction worth under a dollar a year. Price every account in dollars with balance × APY, read 'up to' and teaser offers as puzzles rather than promises, and audit your actual rate annually. Savings interest math is one multiplication — banks just profit from how few people do it.