Compound Interest Calculator – Growth with Compounding

How it works

A nominal rate looks different depending on how often it compounds. This tool finds the equivalent rate at another frequency, and the effective annual rate (APY) after a year of compounding. Use the Future Value calculator to grow a principal over time.

EAR = (1 + r/n)^n − 1 · r_out = m · ((1 + EAR)^(1/m) − 1)

When to use

Use this tool when you need to: default: 6% compounded monthly equals about 6.16778% compounded annually (APY).

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Default: 6% compounded monthly equals about 6.16778% compounded annually (APY).

Frequently asked questions

What is the Compound Interest Calculator?: A nominal rate looks different depending on how often it compounds. This tool finds the equivalent rate at another frequency, and the effective annual rate (APY) after a year of compounding. Use the Future Value calculator to grow a principal over time.
How do I use the Compound Interest Calculator?: Enter the required values, then calculate. The Compound Interest Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Compound Interest Calculator use?: EAR = (1 + r/n)^n − 1 · r_out = m · ((1 + EAR)^(1/m) − 1)

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How it works

What this calculator converts

A 6% rate is not the same true yield if it compounds monthly instead of once a year. This tool converts a nominal annual rate from one compounding schedule to another so both quotes mean the same growth over a year. To grow a principal over time, use the Future Value calculator.

Simple vs compound interest

Simple interest charges only the original principal: $100 at 10% for two years costs $20. Compound interest charges interest on interest. The same $100 at 10% compounded annually becomes $110 after year one and $121 after year two — $21 of interest. Almost all modern loans and savings accounts compound.

APY, APR, and frequency

More frequent compounding raises the effective annual rate. A 6% mortgage quoted monthly is about 6.17% as an annual APY. Lenders often show the monthly (APR-style) figure because it looks lower. Savings accounts and CDs are more often quoted annually. Continuous compounding is the mathematical limit as the number of periods goes to infinity: EAR = e^r − 1.

Formulas and the Rule of 72

Discrete compounding: EAR = (1 + r/n)^n − 1, then the destination rate is m times ((1 + EAR)^(1/m) − 1). Continuous: EAR = e^r − 1 and r = ln(1 + EAR). The Rule of 72 is a rough doubling-time shortcut: years ≈ 72 / percent rate. At 8%, money doubles in about nine years. It is an estimate, not a substitute for the formulas above.

How it works

EAR = (1 + r/n)^n − 1 · r_out = m · ((1 + EAR)^(1/m) − 1)

Frequently asked questions

What is the Compound Interest Calculator?

How do I use the Compound Interest Calculator?

Enter the required values, then calculate. The Compound Interest Calculator shows results, formulas, and step-by-step work when available. No account is required.

What formula does the Compound Interest Calculator use?

EAR = (1 + r/n)^n − 1 · r_out = m · ((1 + EAR)^(1/m) − 1)