Compound Interest Formula Explained: How to Calculate Growth

Learn the compound interest formula step by step, with a worked example, how compounding frequency changes the result, and the effect of regular.

By Michael Hewitt, Founder & Editor-in-Chief. Updated October 27, 2026.

The Formula and What Each Variable Means

Compound interest is interest earned on both the original amount and the interest already added. The standard formula is A = P(1 + r/n)^(nt), where A is the balance at the end, P is the starting amount, r is the annual rate as a decimal, n is how many times per year the interest is added, and t is the number of years.

The rate is written as a decimal, so 5% becomes 0.05. The exponent nt counts compounding periods: ten years compounded monthly is 120 periods.

A Worked Example, Step by Step

Take a starting amount of $1,000 and a hypothetical 5% annual return. No account in this example pays that return; it is there to show the arithmetic.

Compounded once a year for 10 years: A = 1,000 × (1 + 0.05)^10 = 1,000 × 1.62889 = $1,628.89.

Compounded monthly for the same 10 years: A = 1,000 × (1 + 0.05/12)^120 = 1,000 × 1.64701 = $1,647.01.

The monthly version finishes about $18 higher, and the gap widens the longer the money stays invested.

How Compounding Frequency Changes the Result

More frequent compounding adds interest to the balance sooner, so each period's interest starts earning interest in the next period. The effect is real but modest over short periods. Read the stated compounding frequency on any account before comparing it with another. Two accounts that quote the same rate can produce different balances if they compound on different schedules.

Adding Regular Contributions: The Future Value of a Series

Most savers add money over time instead of investing one lump sum. For regular contributions, the future value formula counts the growth on each payment. Using the same hypothetical 5% return, compounded monthly, $100 added at the end of each month for 10 years grows to about $15,528. The contributions total $12,000, so about $3,528 of that is growth.

The earlier a contribution is made, the more periods it has to compound. This is why starting early usually beats starting with a larger amount later.

The Rule of 72 and Other Shortcuts

The Rule of 72 estimates how long money takes to double: divide 72 by the annual return. It is an approximation, and it is most accurate for moderate returns. It gives a quick check on any compound growth calculation, but it does not replace the formula when the numbers matter.

Continuous Compounding and Effective Annual Yield

Some accounts and textbooks use continuous compounding, where interest is added at every instant. The formula becomes A = Pe^(rt), where e is about 2.718. Continuous compounding always gives a slightly higher balance than the same rate compounded monthly, but the difference is small for ordinary rates and short periods.

Comparing accounts with different compounding schedules is easier with the effective annual rate, the rate that would give the same one-year growth with annual compounding. For a nominal rate r compounded n times a year, the effective annual rate is (1 + r/n)^n − 1. A nominal 5% compounded monthly works out to about 5.12% effective, which is why the same quoted rate can produce different balances.

Where the Math Meets Real Accounts

The formula assumes the return is steady and that every dollar of interest stays in the account. Real accounts differ on three points. Rates on savings and money market accounts change over time, so the rate on the day you open an account may not last. Interest is taxable in most accounts, which lowers what you keep. Fees, if any, come out of the balance and reduce the result. Our guide to high-yield savings, money market accounts and CDs compares how each account type handles these points.

Run the Numbers Before Choosing an Account

Use the formula with the rate, compounding frequency and fees from an account's own disclosures, not from a headline figure. Then compare the balance you would reach with and without the account's costs.