How the numbers work

The formula, the method and the limits of the calculator, with the sources.

The formula

The effective annual rate (APY) shows what compounding does in one year.

Let r be the yearly rate as a fraction, and n the number of compounding periods in a year.

For example, a rate of 5% compounded monthly has an APY of 5.116%.

APY = (1 + r / n)^n - 1
Continuous compounding: APY = e^r - 1

Let p be the number of deposit periods in a year. The calculator finds the rate for one deposit period.

This lets you compound daily and deposit monthly, for example. The rate for one deposit period is the equivalent rate.

i = (1 + r / n)^(n / p) - 1
Continuous compounding: i = e^(r / p) - 1

The calculator runs one deposit period at a time.
If the deposit is due at the start, it goes in first.
Then the interest of the period is added to the balance.
If the deposit is due at the end, it goes in last.
The yearly increase of the deposit applies at the start of each new year.
With no deposit, the schedule has 12 rows for each year.
The calculator works in full precision. It rounds to cents only to show a number or to write the CSV file.

Take $10,000.00 at 5% for 10 years, compounded monthly, with no deposits.

The end balance is $16,470.09.

The SEC Investor.gov calculator should give the same number.

The calculator finds the exact years to double your money from the APY.

The rule of 72 is a quick estimate. It divides 72 by the rate in percent.

The rule is close for rates from 4% to 12%. It is less exact outside that range.

years = ln(2) / ln(1 + APY)

The calculator uses one fixed rate for all years. Real returns change from year to year.

It does not include fees, taxes or the risk of a loss. Fees and taxes lower your return.

Inflation is one fixed rate. The balance in today's money is the end balance divided by (1 + inflation)^years.

Banks can round interest each period or use other day counts. Their results can differ by a few cents.

The currency choice changes the symbol only. The calculator does not convert money.

Checked on 2026-11-11.

U.S. SEC Investor.gov: Compound Interest Calculator. An official calculator for the same job. Use it to check our results.
Consumer Financial Protection Bureau: How does compound interest work?. Compound interest is interest on your savings and on the interest you already earned. More frequent compounding makes savings grow faster.
Financial Consumer Agency of Canada: Savings accounts. Banks add interest to your account, and then you earn interest on the new total. Daily compounding can earn more than monthly.
Truth in Savings, Regulation DD (12 CFR 1030), Appendix A. The rule for the annual percentage yield (APY). It is the interest of one year on one dollar, with compounding.
U.S. SEC Investor.gov: What is compound interest?. A classroom page that explains compound interest and the rule of 72.