How to Calculate APY: Annual Percentage Yield Guide
APY is the interest rate you actually earn once compounding is counted. This guide derives the formula, works through examples at every compounding frequency, explains exactly how APY differs from APR and interest rate, and shows how to compare accounts honestly.
How to Calculate APY
Two savings accounts both advertise "5% interest". One pays you more than the other. Neither is lying.
The difference is compounding — how often the bank calculates interest and adds it to your balance. Once interest starts earning interest, the headline rate stops telling you what you actually get.
Annual Percentage Yield (APY) is the number that fixes this. It folds compounding into a single figure, so two accounts can be compared directly.
The formula
APY = (1 + (r)/(n))^n - 1
Where r is the nominal annual interest rate as a decimal, and n is the number of compounding periods per year.
The logic is straightforward. Each period you earn r/n — a twelfth of the annual rate if compounding monthly. Multiplying by (1 + r/n) applies one period's growth. Doing that n times compounds it across the year. Subtracting 1 strips out your original principal, leaving the growth as a rate.
Worked example: the same rate, five different answers
Take a nominal rate of 5% (r = 0.05) and vary only the compounding frequency.
Annually (n = 1):
APY = (1 + 0.05)^1 - 1 = 0.05 = 5.000\%
Quarterly (n = 4):
APY = (1 + (0.05)/(4))^4 - 1 = (1.0125)^4 - 1 = 1.050945 - 1 = 5.0945\%
Monthly (n = 12):
APY = (1 + (0.05)/(12))^12 - 1 = (1.0041667)^12 - 1 = 5.1162\%
Daily (n = 365):
APY = (1 + (0.05)/(365))^365 - 1 = 5.1267\%
Continuously (the theoretical limit):
APY = e^0.05 - 1 = 5.1271\%
Two things are worth noticing.
The gain from more frequent compounding shrinks fast. Moving from annual to quarterly adds 9.45 basis points. Moving from daily to continuous adds 0.04. Beyond monthly, compounding frequency is nearly irrelevant — a bank advertising "compounded daily!" as a headline feature is selling you about £1 a year on £10,000 versus monthly.
There is a hard ceiling. No matter how often you compound, 5% nominal cannot exceed e^0.05 - 1 = 5.127\%. Infinite compounding is a limit, not a loophole.
APY vs APR vs interest rate
These three get used interchangeably in conversation and mean genuinely different things.
Nominal interest rate is the headline rate before compounding is considered. It is the r in the formula above. On its own it is not comparable between accounts.
APY (Annual Percentage Yield) includes compounding. It is what you earn on savings and investments. Higher is better for you.
APR (Annual Percentage Rate) is what you pay on borrowing. It includes fees and charges, but — critically — in most jurisdictions APR does not compound within the year. A credit card quoting 24% APR compounding monthly actually costs:
(1 + (0.24)/(12))^12 - 1 = (1.02)^12 - 1 = 26.82\%
That is nearly three percentage points more than the advertised figure. The equivalent measure for borrowing is sometimes called EAR (Effective Annual Rate), and it is the same calculation as APY.
The asymmetry is not accidental. Lenders quote APR because it looks smaller; savings providers quote APY because it looks larger. Both are legally accurate.
A useful rule: when you are earning, look for APY. When you are borrowing, convert the APR to its effective rate before comparing.
Going the other way: finding the rate from APY
If a provider advertises APY and you need the nominal rate:
r = n[(1 + APY)^1/n - 1]
Example. An account advertises 4.5% APY compounded monthly. The nominal rate is:
r = 12[(1.045)^1/12 - 1] = 12 × 0.0036748 = 4.410\%
So 4.41% nominal, compounded monthly, yields 4.5% APY.
Why this matters more than it looks
Over one year the differences are small. Over decades they are not.
£10,000 at 5% for 30 years:
- Simple interest (no compounding at all): £25,000
- 5.00% APY (annual compounding): £43,219
- 5.1162% APY (monthly compounding): £44,677
- 5.1267% APY (daily compounding): £44,812
The gap between annual and daily compounding is £1,593 — on the same nominal rate, from nothing but how often the bank does its arithmetic.
The far larger gap is between simple and compound interest: £18,219. That is the actual lesson. Compounding frequency is a rounding detail; compounding at all is what builds wealth.
Regular contributions
Most people are not depositing a lump sum and walking away. With a regular contribution PMT each period, the future value becomes:
FV = P(1 + i)^N + PMT × ((1 + i)^N - 1)/(i)
Where i = r/n is the periodic rate and N = n × \textyears is the total number of periods.
Example. £5,000 initial, £200 per month, 5% nominal compounded monthly, 10 years.
i = 0.05/12 = 0.00416667, N = 120, and (1 + i)^120 = 1.647009.
FV = 5000(1.647009) + 200 × (1.647009 - 1)/(0.00416667) FV = 8235.05 + 200 × 155.2822 = 8235.05 + 31056.45 = £39,291.50
Of that, £29,000 is money you put in (£5,000 + 120 × £200) and £10,291.50 is interest earned.
What APY does not tell you
APY is a clean comparison tool, but it quietly assumes several things.
That the rate holds. Most savings accounts pay variable rates. An advertised APY is a snapshot, and introductory or "bonus" rates frequently drop after 12 months. Check whether the rate is fixed, and for how long.
That you meet the conditions. High-yield accounts often require a minimum balance, a minimum number of monthly transactions, or a linked current account. Miss the condition and the rate can collapse to near zero.
That you leave the money alone. APY assumes interest stays in the account and compounds. Withdraw it monthly and you earn the nominal rate, not the APY.
That tax does not exist. APY is quoted gross. If savings interest is taxable at your marginal rate, your real return is lower. A 5% APY taxed at 20% nets 4%.
That inflation is zero. This is the big one. A 5% APY during 6% inflation is a real return of roughly −1%. Your balance grows while your purchasing power shrinks. The approximation is real ≈ nominal − inflation; the exact form is (1 + r)/(1 + i) - 1.
Common mistakes
Comparing APR against APY. They are not the same measure. Convert both to an effective annual rate first.
Assuming a higher compounding frequency is a meaningful benefit. Past monthly, the gains are negligible. Do not choose an account with a worse rate because it compounds daily.
Forgetting to convert percentages to decimals. Using 5 instead of 0.05 in the formula produces nonsense.
Ignoring fees. A monthly account fee of £5 on a £1,000 balance costs 6% a year — more than any savings rate will pay you.
Trusting introductory rates. Calculate the blended return over your actual holding period, not just the first 12 months.
Frequently asked questions
Is a higher APY always better? For directly comparable accounts, yes — that is the point of the measure. But check the conditions attached, whether the rate is fixed or variable, and whether fees erode it.
What is a good APY? It depends entirely on the prevailing base rate. In a low-rate environment 1% may be competitive; when central bank rates are high, 5% may be ordinary. Compare against the current base rate and against inflation, not against a remembered figure from a different era.
Does APY apply to loans? Not conventionally. Loans quote APR. The equivalent compounded figure for borrowing is the Effective Annual Rate, calculated identically to APY.
Why is my actual interest lower than the advertised APY? Common causes: you did not hold the balance for the full year, you withdrew interest instead of letting it compound, the rate changed mid-year, or the advertised rate required conditions you did not meet.
Can APY be lower than the nominal rate? No. Compounding can only add to your return, so APY is always greater than or equal to the nominal rate, with equality when compounding is annual.
How does APY work on a CD or fixed-term deposit? The same formula applies, but the rate is fixed for the term, which removes the variable-rate uncertainty. The trade-off is access: early withdrawal usually forfeits some interest.
Summary
APY converts a nominal rate plus a compounding frequency into a single comparable number: (1 + r/n)^n - 1. It is the figure to use when comparing savings products, and its borrowing counterpart is the effective annual rate, not the advertised APR.
The compounding frequency matters far less than people assume — beyond monthly, it is noise. What matters is the rate itself, the fees, whether the rate persists, and whether it beats inflation.
Compare accounts with our APY Calculator, which shows the effective yield at any compounding frequency.