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Miraç Özdemir
Compound Interest

Effective Interest Rate Calculator (Nominal to Effective)

Convert nominal annual interest to the effective (compound) annual rate and back; get per-period rates and annual compound and simple rates from a monthly rate.

Version 1

Things to keep in mind:

  • Withholding tax, fees and charges are not included; use the deposit or investment withholding tools for net returns.
  • Loan effective cost also includes fees and taxes; use the loan APR tool for loans.
  • Continuous compounding is a theoretical limit; quoted rates are usually daily or monthly compounded.

Calculator

Interest rate

Choose the kind of rate you have: the quoted nominal annual rate, the effective annual rate, or the rate of a single period (month, day, …).

Rate of the selected type in percent. For a daily period rate use at most 20% (larger values overflow the calculation).

How many times per year interest is added to the principal. With continuous compounding the period rate is shown on a daily (1/365) basis.

After the first calculation, the result updates automatically when you change a value.

Result

Enter the values and press Calculate to see the result here.

About this tool

Banks usually quote a nominal annual rate; when interest is added to the principal several times a year, the rate you really earn or pay is the effective annual rate. This tool converts between the two in both directions.

Formulas (m = compounding periods per year)

  • Effective = (1 + nominal / m)^m − 1
  • Nominal = m × ((1 + effective)^(1/m) − 1)
  • Period rate = nominal / m = (1 + effective)^(1/m) − 1
  • Continuous: effective = e^nominal − 1; nominal = ln(1 + effective)
  • From a monthly rate: annual compound = (1 + monthly)^12 − 1, annual simple = monthly × 12
  • Effective minus nominal = effective rate − nominal rate

m is 365 for daily, 12 for monthly, 4 quarterly, 2 semi-annual and 1 annual compounding. Percentages are rounded HALF_UP to 4 decimals.

Example 1

A 45% nominal annual rate compounded monthly gives a 3.75% period rate and an effective annual rate of (1.0375)^12 − 1 = 55.5454%, a gap of 10.5454 points. A 4.5% monthly rate equals 69.59% compound or 54% simple per year.

Example 2 — the effect of compounding frequency

A 40% nominal annual rate reaches an effective 49.1498% with daily compounding and 49.1825% with continuous compounding. A 30% nominal rate compounded semi-annually is 32.2500% effective.

Example 3 — effective to nominal

A 60% effective annual rate corresponds to a nominal 49.8731% with quarterly compounding; the period rate is 12.4683% and the equivalent monthly compound rate 3.9944%.

How to read the result

The effective annual rate is the true annual rate that lets you compare offers with different compounding on one scale; the more often interest compounds, the further it moves above the nominal rate. "Effective minus nominal" is the extra points compounding adds and grows as rates rise. The equivalent monthly rate converts the annual return into its monthly compound equivalent. Results exclude withholding tax and fees.

How to use

  1. Choose the type of rate you have (nominal, effective or per-period).
  2. Enter the rate in percent.
  3. Choose the compounding frequency (daily, monthly, quarterly, semi-annual, annual or continuous).
  4. Press Calculate to see the effective, nominal and period rates.

Notes

Percentages are rounded HALF_UP to 4 decimals. Daily compounding uses 365 days; actual day counts, value dates and withholding are ignored. "Nominal (simple)" is the period rate times periods per year.

Sources

Frequently asked questions

4 questions

  1. The nominal rate is quoted without compounding effects. The effective rate includes interest being added to the principal during the year, so it exceeds the nominal rate as compounding gets more frequent.

Next step

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