APY Calculator

The Formula

APY (Annual Percentage Yield) shows the real annual return on savings once compounding is taken into account, which is why it's almost always higher than the stated interest rate. The formula is APY = (1 + r/n)^n − 1, where r is the nominal annual rate (as a decimal) and n is the number of compounding periods per year. The key insight is that interest earns interest: when interest is added to your balance partway through the year, the later interest is calculated on the slightly larger balance, so you end up with more than the simple rate suggests. A worked example: a 5% nominal rate compounded monthly gives APY = (1 + 0.05/12)^12 − 1 = 0.05116, or 5.116% — slightly more than 5% because each month's interest joins the balance and earns more. The more frequently interest compounds, the higher the APY relative to the nominal rate: annual compounding gives exactly 5%, monthly gives 5.116%, and daily gives about 5.127%. The difference seems small at 5%, but it grows with higher rates and larger balances, and compounds dramatically over many years. This calculator works out the true APY so you can compare accounts on an equal footing.

Why Banks Use APR

Understanding the difference between the nominal rate and APY protects you when comparing financial products, because providers choose whichever figure looks better for them. The nominal rate (often called APR) is the headline rate without compounding, while APY (or AER in the UK — Annual Equivalent Rate) includes compounding and shows the true return. For savings, the APY/AER is the higher, more attractive figure, so banks tend to advertise it for savings accounts. For borrowing, the situation reverses: lenders advertise the lower APR, even though the effective cost you pay with compounding is higher. The practical rule: when comparing savings accounts, always compare APY/AER, because it accounts for how often interest compounds and lets you compare like with like — an account paying 4.9% compounded daily can beat one paying 5.0% paid annually. In the UK, providers must quote the AER for savings precisely so consumers can compare fairly. When borrowing, compare APRs, and check whether the headline rate includes all fees. The compounding frequency matters most at higher balances and rates, where small percentage differences translate into meaningful money over time.

Continuous Compounding

Continuous compounding represents the theoretical maximum return as compounding frequency increases without limit — compounding not just daily or hourly but instantaneously. The formula uses the mathematical constant e (approximately 2.71828): APY = e^r − 1. At a 5% nominal rate, continuous compounding gives APY = e^0.05 − 1 = 0.05127, or 5.127%. Notice this is only marginally higher than daily compounding (5.127% vs about 5.127% — they're nearly identical), which illustrates an important point: there are diminishing returns to compounding more frequently. Going from annual to monthly compounding makes a noticeable difference; going from daily to continuous makes almost none. So while continuous compounding is the mathematical ceiling, real-world accounts using daily or monthly compounding get very close to it already. Continuous compounding appears more in finance theory, options pricing, and academic contexts than in everyday savings accounts, which use discrete periods (daily, monthly, quarterly, or annually). The concept is useful for understanding the upper limit of what compounding can achieve, and for certain financial calculations, but for comparing real savings accounts, the discrete APY/AER is what matters. This calculator can show the effect of different compounding frequencies so you can see how much (or how little) it changes the outcome.

When to Seek Financial Advice

Calculator results provide estimates based on the figures you enter and shouldn't replace professional advice for significant financial decisions. APY calculations assume the rate stays constant, but many savings accounts have variable rates that can change, and introductory bonus rates often drop after 12 months — so the APY you start with may not be what you earn long-term. For everyday savings comparisons, the APY/AER figure is enough to choose between accounts. For larger decisions — where to invest a substantial sum, balancing savings against paying down debt, or tax-efficient saving — it's worth getting guidance. In the UK, free and impartial money guidance is available through MoneyHelper (moneyhelper.org.uk), a government-backed service. For personalised, regulated advice on investments, pensions, and larger financial planning, a regulated independent financial adviser (IFA) can help — you can find one through unbiased.co.uk. Remember that with savings, you should also consider inflation: if your APY is below the inflation rate, your money is losing real purchasing power even as the balance grows, which matters for longer-term savings. And check whether interest pushes you over your Personal Savings Allowance, beyond which savings interest is taxable. This isn't financial advice — it's general information to help you understand how APY works.