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APY Calculator

Convert an advertised nominal rate into the annual percentage yield you actually earn once compounding is counted.

Inputs
APY resultCalculated
APY5.1162%
Formula
APY(1 + r / n) ^ n - 1
Inputs
rnominal annual rate 5.00%
ncompounding periods 12 (monthly)
deposit10,000.00
Working
r / n0.05 / 12 = 0.0041666667
(1 + 0.0041666667) ^ 121.0511618979
APY1.0511618979 - 1 = 0.0511619
Results
  Annual percentage yield             5.1162%
  Nominal rate (APR)                  5.0000%
  Compounding gain over APR           0.1162%
  Interest on the deposit in 1 year   511.62
  Balance after 1 year                10,511.62
Runs locally in your browser

About the APY Calculator

Two savings accounts can quote the same headline rate and pay different amounts, because one credits interest monthly and the other only once a year. Annual percentage yield settles the argument by folding the compounding schedule into a single comparable number. A nominal 5 percent compounded monthly works out at 5.1162 percent APY, which is 5.62 of extra interest on a 10,000 balance over twelve months.

The tool asks for the nominal rate, how often interest is credited and an optional balance. It prints the per period rate, the compounding factor and the yield, so the chain from 0.05 divided by 12 through to 1.0511618979 is all on screen. Raising the frequency raises the yield, but the gain shrinks quickly: moving from monthly to daily on a 5 percent rate adds only about four hundredths of a percentage point.

Banks in many countries must quote APY or its local equivalent on deposit products, so if a provider only advertises a nominal figure this converts it into something you can line up against the rest of the market. For a fixed term deposit where you also want the maturity value, the CD Calculator runs the same maths over a set number of months. For borrowing rather than saving, the EAR Calculator shows the same idea from the payer side.

How to use

  1. Enter the nominal annual rate the provider advertises.
  2. Pick how often interest is added: daily, weekly, monthly, quarterly, half yearly or yearly.
  3. Optionally type a deposit amount to see the cash interest for one year.
  4. Compare the APY line against another account quoted the same way.

Common questions

What is the difference between APR and APY?
APR is the plain nominal rate with no compounding applied. APY adds the effect of interest being credited during the year, so it is always equal to or higher than APR.
What is the APY formula?
APY = (1 + r / n) ^ n - 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods in a year.
Does daily compounding really help?
Only slightly. At 5 percent nominal, daily compounding yields about 5.1267 percent against 5.1162 percent monthly, a difference of roughly one dollar per 10,000 saved.
Is the interest figure guaranteed?
No. It assumes the rate and the balance both stay fixed for a full year, which variable rate accounts do not promise.