Two banks advertise savings accounts. One says 4.5 percent. The other says 4.6 percent. The second one is better, right?
Not necessarily. One number might be a plain rate and the other a yield that includes compounding. The annual percentage yield, or APY, puts everything on the same footing: it’s what you actually earn in a year once interest on interest is counted. This APY calculator converts in both directions.
How to use the APY Calculator#
- Choose the direction. Pick interest rate to APY, or APY to interest rate.
- Enter the rate or the APY. Use the number the bank quotes.
- Pick the compounding. Choose how often interest is added to your balance.
- Add a deposit and years (optional). This shows what the yield means in money.
- Read the result. You get the converted figure and, if you wish, the balance and interest earned.
The formula#
The rate is the stated yearly rate as a decimal, and n is the number of times interest is added per year. At 4.5 percent compounded monthly, n is 12 and the APY is (1 + 0.045 ÷ 12) ^ 12 − 1, which comes to 4.594 percent. That’s the number to compare across banks.
To go the other way, the calculator reverses it. An APY of 4.6 percent with monthly compounding corresponds to a stated rate of 4.506 percent.
Compounding frequency in numbers#
This table shows how a 5 percent stated rate turns into APY as the compounding gets more frequent:
| Interest added | Times per year | APY |
|---|---|---|
| Once a year | 1 | 5.0000% |
| Twice a year | 2 | 5.0625% |
| Quarterly | 4 | 5.0945% |
| Monthly | 12 | 5.1162% |
| Daily | 365 | 5.1267% |
The gain levels off. There’s a mathematical limit called continuous compounding, where the APY is e to the power of the rate, minus one. At 5 percent that gives 5.1271 percent, barely above daily.
APY versus APR#
The two names describe the same idea from different sides. APR, the annual percentage rate, is the stated yearly rate without compounding. APY includes it. Lenders tend to advertise APR on loans and credit cards, which makes the cost look lower than the true yearly figure. Banks tend to advertise APY on savings, which makes the return look higher. Both are legitimate, and both are worth converting if you want a fair comparison.
What it means in money#
With a deposit of 10,000 at 4.5 percent compounded monthly, the APY is 4.594 percent. After one year the balance is 10,459.40, and the interest is 459.40. Leave it for three years and the same APY compounds on itself each year. Use the deposit and years boxes to try it with your own numbers.
If your money is in a fixed-term account, the CD calculator shows the balance at maturity directly.
Things the APY doesn’t tell you#
- Whether the rate is fixed or variable. Many savings accounts change their rate whenever the bank decides.
- Fees, minimum balances or limits on withdrawals that eat into the return.
- Tax on the interest, and inflation.
The same 6 percent, six ways#
A nominal rate of 6 percent a year gives different yields depending on how often interest is added. The more often, the higher the yield, but the gains flatten out quickly.
| Compounding | APY on a 6% rate |
|---|---|
| Annually | 6.000% |
| Semi-annually | 6.090% |
| Quarterly | 6.136% |
| Monthly | 6.168% |
| Daily | 6.183% |
| Continuously | 6.184% |
Going from annual to monthly adds 0.168 points. Going from monthly to daily adds only 0.015. Continuous compounding is the mathematical limit and would add 0.001 more. For comparing accounts, the frequency matters far less than the headline rate.
Comparing two offers#
Account A pays 4.5 percent compounded daily, and account B pays 4.55 percent compounded annually. The APY of A is (1 + 0.045 ÷ 365)^365 − 1 = 4.602 percent, and B is 4.550 percent. B is better by -0.052 points. On ₦1,000,000 for a year, that is about ₦-525 extra. Look also at fees, minimum balances, how long the rate is guaranteed and whether it is a promotional rate that falls after a few months.
Frequently asked questions#
Use APY = (1 + rate ÷ n) ^ n − 1, where n is the number of compounding periods per year. A 4.5 percent rate compounded monthly gives 4.594 percent.
APR is the stated rate without compounding. APY includes compounding, so it’s equal to or higher than the APR.
For the same account type and risk, yes. Check whether the rate is fixed, and watch for fees and withdrawal limits.
Use rate = n × ((1 + APY) ^ (1 ÷ n) − 1). The calculator does this when you choose APY to interest rate.
Only a small one. Going from yearly to daily compounding at 5 percent adds about 0.13 percentage points.
No. APY only measures interest and compounding. Fees, taxes, penalties and inflation reduce what you keep. If an account charges a monthly fee, subtract it from your interest to find the true return, and check whether the interest is taxed where you live.