APY Calculator

Have the rate and the compounding schedule from your account terms to hand. If the schedule is not stated, daily and monthly are the most common choices for savings products.

1. In The rate I know is, choose APR (nominal rate) if you have the stated rate, or APY (effective annual yield) if you have the yield.
2. Type the figure in Rate (%), for example 4.25.
3. Pick how often interest is added in Compounded: Daily, Monthly, Quarterly, Twice a year, Yearly or Continuously.
4. Optionally fill in Deposit (optional) and Years (optional) to see the ending balance and interest earned.
5. Read the large figure, which is the other rate, then the rows that show both rates and the extra yield from compounding.

If you leave the deposit or years at zero, the tool still converts the rate and simply skips the balance and the year-by-year table.

The compounding choice matters when you know the APR but not the schedule. Banks usually state the schedule in the account terms, and an APY quoted by the bank already includes it. If you only have an APY, the schedule affects the APR you get back but not the balance, because the balance table grows the deposit at the APY itself. Fractional years such as 2.5 are allowed.

The APR here is the nominal annual rate, before interest is added on top of interest. The APY is the effective rate after compounding, which is why it is never lower than the APR. The relationship is:

• APR to APY: APY = (1 + APR / n)^n - 1, where n is the number of compounding periods a year
• Continuous compounding: APY = e^APR - 1
• APY to APR: APR = n x ((1 + APY)^(1/n) - 1)

For example, 4.25 percent APR compounded daily (n = 365) gives (1 + 0.0425 / 365)^365 - 1 = 4.3413 percent APY. The extra yield from compounding is 0.0913 percentage points. With a 10,000 deposit for 5 years the balance is 10,000 x 1.043413^5 = 12,367.51, so the interest earned is 2,367.51. Going the other way, a 5 percent APY compounded monthly corresponds to a 4.8889 percent APR. These rates are examples, not current offers.

The more often interest compounds, the higher the APY for the same APR, but the gains shrink quickly:

APY is useful because it puts accounts with different compounding schedules on the same footing. Compare an APY with an APY, or convert both to the same basis first. Putting an APR next to an APY makes the second one look better than it is. On loans, an APR can also include fees, but in this tool APR always means the nominal rate only.

A quick comparison shows why this matters. Suppose account A advertises 4.25 percent APR compounded daily and account B advertises 4.30 percent APY. Account A converts to 4.3413 percent APY, so it earns slightly more than B even though its headline number looks lower. On 10,000 for 5 years that gap is the difference between 12,367.51 and about 12,343, an example with invented accounts to show the method.

The balance table assumes you add and withdraw nothing and that the rate never changes. Real savings rates are often variable, so the actual balance can differ. The figures are mathematical results, not a bank statement, and they ignore tax, account fees and minimum balances. They are an estimate for general information and not financial or tax advice.

If you want to see growth with regular contributions, use the compound interest calculator. To see the contrast with interest that never compounds, try the simple interest calculator. The savings goal calculator works out how much to set aside each month, and the ROI calculator measures the return on any investment once you know what it returned.