How do you calculate APY?
Divide the interest rate by the number of times it compounds in a year, add 1, raise that to the number of compounding periods, and subtract 1. A 4% rate compounded monthly is (1 + 0.04 ÷ 12)12 − 1, or 4.074% APY. Compounded daily, the same rate is 4.081%.
APY = (1 + r ÷ n)n − 1
r is the yearly interest rate and n the compounding periods in a year: 12 for monthly, 365 for daily. With continuous compounding, the limit as n grows without end, APY = er − 1.
“What’s the APY on a 4% interest rate compounded monthly?”
4.074%. On $10,000 that’s $407.42 in a year instead of $400. Try this scenario
APY vs. interest rate: what’s the difference?
The interest rate is the yearly rate before compounding, sometimes called the APR or nominal rate. The APY is what you actually earn over a year once interest is added to the balance and starts earning interest itself. They’re equal only when interest compounds once a year; otherwise the APY is higher.
Use APY to compare savings accounts and CDs, since it already counts compounding. The gap grows with the rate: tiny at 1%, noticeable at 10% and above.
Is 1% a month the same as 12% a year?
No. Earning 1% a month and letting it compound gives 12.683% over a year, because each month’s interest is earned on a slightly bigger balance. 12% is what you’d get only if the interest were never added to the balance. The higher the monthly rate, the wider that gap: 2% a month is 26.824% a year.
“Is 1% interest per month the same as 12% per year?”
No, it’s 12.683% a year once it compounds. Try this scenario
How do I convert APY to an interest rate?
Work the formula backward: add 1 to the APY, take the n-th root, subtract 1 and multiply by n. A 5% APY compounded daily comes from a 4.879% interest rate; compounded monthly, from 4.889%. Set the calculator to APY to do this for any rate and frequency.
Rate = n × ((1 + APY)1 ÷ n − 1)
“My bank advertises 5% APY, compounded daily. What’s the actual interest rate?”
4.879%. Compounding daily turns it into 5% over a year. Try this scenario
Does it matter whether interest compounds daily or monthly?
Barely. At 4%, annual compounding gives 4.000% APY, quarterly 4.060%, monthly 4.074% and daily 4.081%. Even continuous compounding only reaches 4.081%. On $10,000 the step from monthly to daily is worth about 66 cents a year, so pick an account on its APY, not on how often it compounds.
“What does daily compounding add to a 4% rate?”
It makes the APY 4.081%, against 4.074% for monthly. Try this scenario
APY works against you on debt
Credit cards quote an APR, but interest is usually charged daily on the balance, so a balance you carry grows faster than the APR suggests. A 24% APR compounded daily is a 27.115% APY. Run your card’s APR through the calculator with daily compounding to see what carrying a balance really costs.
“My credit card charges 24% APR. What’s that as a yearly rate with compounding?”
27.115%, if interest compounds daily and you pay nothing down. Try this scenario
To see how long a card balance takes to clear, use the debt payoff calculator. To see what a savings APY earns with monthly deposits, use the high-yield savings calculator.
APY FAQ
How do I calculate APY from the interest I actually earned?
Divide the interest by the principal, add 1, raise it to 365 divided by the days in the term, and subtract 1. That’s the Truth in Savings formula. The rule’s own example: $30.37 earned on $1,000 over a 182-day CD works out to a 6.18% APY.
Is a higher APY always better?
For the same balance and term, yes: APY already includes compounding, so it’s the fairest way to compare accounts. Check the conditions, though. Some high rates apply only up to a balance cap, need a minimum balance or monthly activity, or last only for a promotional period.
Does APY change over time?
On savings and money market accounts, yes: the rate is variable and usually moves with the Federal Reserve’s rate. A CD’s APY is fixed for the term, as long as you don’t withdraw early. That’s the main reason to choose a CD over a savings account.
Why do banks show APY but lenders show APR?
Federal rules require it. Truth in Savings has banks state deposit rates as an APY, which includes compounding and looks higher. Truth in Lending has lenders state loan costs as an APR, which leaves out compounding on most loans and looks lower. Each puts its best number forward.
The formulas are on the methodology page.