Effective Interest Rate Calculator

Key terms

• Nominal annual rate (APR): the stated yearly rate, which is divided among the compounding periods in the year. It does not account for compounding.
• Effective annual rate (EAR): what money actually earns or costs over one year once interest is added to the balance. On savings accounts and CDs it's called the APY (annual percentage yield).
• Compounding frequency: how often interest is added to the balance: annually, semiannually, quarterly, monthly, semimonthly, weekly, daily or continuously.
• Periodic rate: the nominal rate divided by the number of periods per year, for example the monthly rate.

Conversion formulas

EAR = (1 + APR ÷ n)^n − 1
APR = n × ((1 + EAR)^(1/n) − 1)
Continuous compounding: EAR = e^APR − 1

With annual compounding (n = 1), the effective rate equals the nominal rate. The more often interest compounds, the higher the effective rate, with continuous compounding as the upper limit.

How to read the results

• EAR − APR difference: how much compounding adds. The gap widens quickly at higher rates.
• Comparing two rates: convert both to an effective rate. For a loan, the lower EAR is cheaper; for savings, the higher APY earns more.

Two offers with the same nominal rate but different compounding are not equivalent. Comparing nominal rates directly can be misleading.

APR vs. APY in practice

Lenders usually advertise the APR, while banks advertise savings products by APY. The APY is the effective rate, so it is always equal to or higher than the nominal rate. For example, 5% compounded daily is a 5.13% APY, and 5% compounded monthly is a 5.12% APY.

A loan's disclosed APR can also include certain fees, so it is not always a pure nominal interest rate. This calculator converts interest rates only.

When to use it

• Comparing savings accounts, CDs or investments that quote rates with different compounding.
• Finding the true annual cost of a credit card or loan that quotes a nominal APR.
• Getting the nominal rate that matches a known effective rate, for example to enter it in another calculator.

Example

Account A pays 12% compounded monthly. The monthly rate is 1% and the effective annual rate is 12.6825%. Account B pays 12.5% compounded annually, an effective rate of 12.5%. Even though B's stated rate is higher, A earns more: about 0.18 percentage points more per year.

1. Monthly rate = 12% ÷ 12 = 1%
2. EAR for A = (1 + 0.01)^12 − 1 = 12.6825%
3. EAR for B = 12.5% (annual compounding)
4. Difference = 12.6825% − 12.5% ≈ 0.18 points in favor of A

Common mistakes

• Comparing nominal rates with different compounding as if they were the same.
• Multiplying a monthly rate by 12 and calling it the effective annual rate. That gives the nominal rate, not the effective one.
• Assuming the effective rate includes fees or insurance. It only reflects interest and compounding.
• Mixing up APR and APY when comparing a loan with a savings product.