Two savings accounts with the same interest rate but different annual yields due to compounding
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What is APY?

Why two savings accounts with the same rate can pay you different amounts.
Written & fact-checked by the StupidGames editorial team Last updated: June 2026 About the team
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When you're comparing savings accounts, you'll see a number labelled APY — annual percentage yield. It sounds like just another rate, but it's the only rate that tells you what you'll actually earn. Two accounts can advertise the exact same interest rate and pay you meaningfully different amounts, depending on how often that interest compounds. APY is the number that flattens that confusion into a single, honest comparison.

What APY actually means

Annual percentage yield is the effective rate of return you earn on a deposit over one full year, once compounding is factored in. Compounding means that interest you earn gets added to your balance, and then that larger balance earns interest — so your money grows on itself, not just on the original amount.

The more often interest is added to your account — daily, monthly, quarterly — the more opportunities for that compounding effect to stack up. By the end of the year, a nominally identical rate compounds to a slightly higher real return depending on frequency. APY captures that final number.

The formula

The math behind APY is straightforward:

APY = (1 + r/n)n − 1

Where r is the nominal (stated) annual interest rate as a decimal, and n is the number of compounding periods per year.

Say a savings account offers a nominal rate of 5%, compounded monthly (n = 12). Plug it in:

APY = (1 + 0.05/12)12 − 1 ≈ 0.05116, or about 5.12%

That extra 0.12 percentage points is the compounding benefit. On a hypothetical $10,000 deposit, that gap is around $12 in a year — small in isolation, but it widens with larger balances and longer time horizons.

Now compare that to daily compounding (n = 365) at the same 5% nominal rate:

APY = (1 + 0.05/365)365 − 1 ≈ 0.05127, or about 5.13%

The difference between monthly and daily compounding at this rate is tiny. The bigger lever is the nominal rate itself — but when rates are similar, compounding frequency is the tiebreaker.

APY calculator
APY
Balance
Interest earned

Estimate only — assumes the rate and compounding stay constant, with no extra deposits or fees.

APY vs APR: what's the difference?

APR (annual percentage rate) is a simpler beast: it's the interest rate expressed on an annual basis, without adjusting for compounding. It's what you see on credit cards and most loan offers.

The key contrast:

This is why savings accounts and money market accounts advertise APY — it's the higher, more flattering number — while lenders advertise APR, which is the lower, more flattering number. Neither is dishonest in isolation; you just need to know which one you're looking at and what it includes.

Why the law requires APY disclosure

Before federal regulation standardised this, comparing savings accounts was a headache. Banks used different compounding schedules, different calculation methods, and sometimes confusingly similar-sounding terms. Congress fixed this with the Truth in Savings Act, implemented by the Federal Reserve's Regulation DD. Under these rules, depository institutions must disclose APY in a consistent, standardised format whenever they advertise a rate on a deposit account.

The result: you can compare a high-yield savings account at one bank against a certificate of deposit at another, and know the APY figures are calculated the same way. It's one of the more consumer-friendly pieces of financial regulation — the comparison does the work for you.

High-yield savings accounts

Online banks and some credit unions often offer savings accounts with significantly higher APYs than traditional brick-and-mortar banks. Because they have lower overhead, they can pass more of the interest income to depositors. The APY on these accounts is variable — it moves with the broader interest-rate environment — so the figure advertised today may not be what you earn next year. Always check the current rate directly with the institution, and look for whether the advertised APY applies to the full balance or only to certain tiers.

What to watch for when shopping accounts

APY makes comparison easier, but a few things can still muddy the picture:

None of this makes APY unreliable — it's still the most honest single number for comparing deposit accounts. It just means a slightly deeper look pays off before you move your money.

A worked example

Say you deposit a hypothetical $5,000 in a savings account advertising a 4% APY, compounded monthly. After one year — assuming no additional deposits or withdrawals — your balance would be approximately $5,204. The $204 in interest reflects what that 4% APY actually delivers. Run the same $5,000 through a simple 4% non-compounding calculation and you'd get exactly $200. The $4 difference is the compounding effect, and it grows the longer you leave the money untouched.

Over several years, the gap compounds on itself. This is why "start early, leave it alone" advice isn't just motivational — it's arithmetic.

Sources & further reading

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