APY calculator

What this number means

APY is what a rate is actually worth over a year once the compounding is counted. A nominal rate is the headline before that. The gap between them is entirely down to how often interest is added to the balance.

The reason this matters is comparison. Two accounts quoting different nominal rates at different frequencies are not directly rankable. Expressed as APY, they are. That is the whole purpose of the measure and the reason the disclosure is required by law.

How this is calculated

Nominal rate to APY:

• APY = (1 + r/n)^n - 1

And back the other way:

• r = n x ((1 + APY)^(1/n) - 1)

In both, r is the nominal annual rate as a decimal and n is the number of compounding periods in a year. The two are exact inverses, so converting one way and then back returns the number you started with.

When the compounding is annual, n is 1 and the two expressions collapse to the same thing. That is why the distinction is invisible until the frequency changes, and why so many people meet it for the first time when two calculators disagree.

APY is defined by the Truth in Savings Act and Regulation DD, 12 CFR 1030, Appendix A, which specifies this calculation for US deposit accounts.

What this does not account for

• Fees. A monthly maintenance fee can wipe out the difference between two APYs and more.
• Promotional rates. An introductory APY that reverts after a few months is not the rate you will earn over a year, whatever it says.
• Balance tiers and minimums. Many accounts quote their best rate only above a threshold, or only up to a cap.
• Tax. APY is a pre-tax figure.
• Rates that move. A savings or money market rate is variable, so today's APY is a snapshot rather than a forecast.

Questions

What is the difference between APR and APY?

APY includes the effect of compounding and APR does not. A nominal rate of 5 percent compounded monthly earns 5.1162 percent over a year, because each month of interest starts earning interest itself. APY is that 5.1162 figure. APR is the 5.

Which one will my bank quote?

For deposit accounts, US banks are required to quote APY. That requirement comes from the Truth in Savings Act, and it exists precisely so that accounts with different compounding frequencies can be compared on one number. For loans and credit cards you are quoted APR instead, under a different rule.

So is a higher APY always better?

For comparing two deposit accounts over the same period, yes, that is what the measure is for. It does not tell you about minimum balances, fees, whether the rate is promotional and expires, or whether the money is locked up. A 5.2 percent APY that drops to 0.5 after three months is worse than a steady 4.5.

How much does compounding frequency actually change things?

Less than most people expect. At 5 percent nominal, daily compounding gives 5.12675 percent APY and monthly gives 5.11619 percent. On 10,000 dollars over a year that is about one dollar and six cents. The frequency is worth understanding so you convert correctly; it is rarely worth choosing an account over.