# What is my effective interest rate?

Converts a stated (nominal) interest rate to its effective annual rate for daily, monthly, quarterly, twice-yearly, yearly or continuous compounding, and back.

- Page: https://www.acalculator.org/finance/effective-interest-rate-calculator
- JSON spec: https://www.acalculator.org/finance/effective-interest-rate-calculator.json
- Version: c9b3c4cd324a

## Default answer

Example with the default inputs (Stated interest rate 6%, Interest is compounded monthly): A stated rate of 6% compounded monthly is an effective annual rate of 6.168%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| rate | Stated interest rate | The nominal yearly interest rate before compounding (the rate quoted, or the APR for a loan). |
| ear | Effective annual rate (EAR) | The rate actually earned or paid in a year once compounding is counted, as a percent. |
| comp | Interest is compounded | How often interest is added to the balance: daily (365 times a year), monthly, quarterly, twice a year, yearly or continuously. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| rate | Stated interest rate | The nominal yearly interest rate before compounding (the rate quoted, or the APR for a loan). |
| ear | Effective annual rate (EAR) | The rate actually earned or paid in a year once compounding is counted, as a percent. |

## Method

EAR = (1 + r ÷ n)^n − 1, where r is the stated yearly rate and n the times interest is compounded a year; EAR = e^r − 1 for continuous compounding. Back: r = n × ((1 + EAR)^(1/n) − 1), or ln(1 + EAR).

## Assumptions

- The stated rate stays the same for the whole year, and interest is added to the balance at each compounding.
- Daily compounding uses 365 days a year.
- No fees. For a savings account the effective annual rate is the annual percentage yield (APY).

## Worked examples

1. rate = 6%, comp = 12 gives ear = 6.167781%. Source: Regulation DD (Truth in Savings), 12 CFR part 1030, appendix A, Part I ($61.68 of interest on $1,000 for a 365-day year is an annual percentage yield of 6.17%). https://www.law.cornell.edu/cfr/text/12/appendix-A_to_part_1030, retrieved 2026-10-02.
2. rate = 12%, comp = 4 gives ear = 12.550881%.
3. rate = 18%, comp = 365 gives ear = 19.716424%.
4. ear = 10%, comp = 12 gives rate = 9.568969%.
5. rate = 5%, comp = continuous gives ear = 5.12711%.

## FAQ

### What is the effective interest rate?

The rate you actually earn or pay in a year once compounding is counted: interest earned on earlier interest. A 6% rate compounded monthly earns 6.168% in a year, so its effective annual rate (EAR) is 6.168%.

### How do I calculate the effective annual rate?

EAR = (1 + r ÷ n)^n − 1, where r is the stated yearly rate as a decimal and n is how many times a year interest is compounded. For 12% compounded quarterly: (1 + 0.12 ÷ 4)^4 − 1 = 1.03^4 − 1 = 12.551%.

### Is the effective interest rate the same as APY?

For a savings account, yes: the annual percentage yield (APY) that banks must show under Regulation DD is the effective annual rate of the account. The same formula applies to a loan, where it shows what the stated rate really costs in a year.

### Is the effective interest rate the same as APR?

No. The APR on a loan is a yearly rate without compounding (and includes some fees). A credit card with an 18% APR that compounds daily has an effective annual rate of about 19.72%.

### How do I find the stated rate from an effective rate?

Reverse the formula: r = n × ((1 + EAR)^(1/n) − 1). An effective rate of 10% with monthly compounding needs a stated rate of 12 × (1.10^(1/12) − 1) = 9.569%.

### What does continuous compounding give?

The limit of compounding more and more often: EAR = e^r − 1. At 5% this is 5.1271%, only a little more than the 5.1267% of daily compounding.

## Sources

- Regulation DD (Truth in Savings), 12 CFR part 1030, appendix A, Part I: annual percentage yield = 100 [(1 + Interest/Principal)^(365/Days in term) − 1]; $61.68 of interest on $1,000 over 365 days is 6.17%. https://www.law.cornell.edu/cfr/text/12/appendix-A_to_part_1030 (retrieved 2026-10-02)
- Consumer Financial Protection Bureau, Regulation DD, 12 CFR 1030.2: definition of annual percentage yield. https://www.consumerfinance.gov/rules-policy/regulations/1030/2/ (retrieved 2026-10-02)