Effective Interest Rate (APY) Calculator
Turn a quoted rate and its compounding frequency into the effective annual rate (APY) you actually earn or pay, or work back from an APY to the nominal rate.
Effective Annual Rate (APY)
6.1678%
Nominal Annual Rate
6%
Rate per Compounding Period
0.5%
Interest on the Balance over One Year
$61.68
How it works
A quoted annual rate is a nominal rate: it says how much interest accrues in a year before compounding. When interest is added to the balance several times a year, each addition earns interest of its own, so the balance grows by more than the nominal rate. The effective annual rate is what the balance actually grows by in one year.
For savings accounts and CDs in the US the effective annual rate is disclosed as the annual percentage yield (APY), defined in the Truth in Savings Act's Regulation DD. Loans quote an APR, which is a nominal rate; the effective rate of a loan's APR shows its true annual cost with compounding.
The calculator divides the nominal rate by the number of compounding periods, compounds that periodic rate for one year, and subtracts the starting balance. Continuous compounding is the limit as the periods become infinitely small, which gives e raised to the nominal rate, less one. Working back from an APY reverses the same steps.
Formula
EAR = (1 + r ÷ n)^n − 1 r = nominal rate, n = periods a year EAR = e^r − 1 continuous compounding r = n × ((1 + EAR)^(1 ÷ n) − 1) nominal from EAR r = ln(1 + EAR) continuous compounding interest over one year = balance × EAR
Example
A 6% nominal rate compounded monthly is 0.5% a month. Compounded for twelve months that is (1.005)^12 − 1 = 6.1678%, so $1,000 earns $61.68 in a year. Regulation DD's own APY example, $61.68 of interest on $1,000 over 365 days, gives the same 6.17% APY.
Excel's EFFECT example: 5.25% compounded quarterly is an effective rate of 5.3543%. Going back with NOMINAL, an APY of 5.3543% compounded quarterly is a nominal rate of 5.2500%.
Assumptions and limitations
- The rate is fixed for the whole year and every period's interest stays in the balance to compound.
- Daily compounding uses 365 periods a year. Some institutions use 360 or count actual days in a leap year, which moves the result slightly.
- A deposit's disclosed APY under Regulation DD (12 CFR 1030, Appendix A) is computed from the actual interest and days in the term; for a one-year term with a fixed rate it equals the effective rate shown here.
- Fees, taxes and minimum balance requirements are not included.
- Results are estimates for planning and education and are not financial, tax or legal advice. Rely on your bank's or lender's disclosure for the figure that applies to you.
Frequently asked questions
Why is the APY higher than the rate my bank quotes?
The quoted rate is nominal. Each time interest is credited it starts earning interest too, so over a year the balance grows by a little more than the nominal rate. The APY includes that compounding; the more often interest is credited, the bigger the gap.
Is a loan's APR the same as its effective rate?
No. APR is a nominal annual rate: the monthly rate times twelve. Its effective annual rate, with monthly compounding, is higher. For comparing loans with the same payment frequency, APR is enough; the effective rate matters when comparing different compounding frequencies.
More in Finance calculators.