How Compound Interest Works: Frequency, APY and Time

The formula, what monthly versus daily compounding is worth (56 cents between daily and continuous on $10,000), how APY compares accounts, and the rule of 72 checked against the exact doubling time.

The Idea in One Example

Compound interest means earning interest on interest. The Consumer Financial Protection Bureau’s example: $1,000 at 5% compounded once a year earns $50 in the first year, giving $1,050, and then 5% of $1,050, or $52.50, in the second, giving $1,102.50. The second year earns more because the first year’s interest is now earning too. Over long periods that difference becomes most of the balance.

The Formula

For a single deposit, A = P(1 + r/n)^nt, where P is the starting amount, r the yearly rate as a decimal, n the number of times interest is added per year and t the years. $10,000 at 5% compounded monthly for 10 years is 10,000 × (1 + 0.05/12)¹²⁰ = $16,470.09. Our Compound Interest Calculator uses this formula and extends it to monthly deposits and withdrawals.

How Much Compounding Frequency Matters

More frequent compounding helps, but less than people expect. The same $10,000 at 5% for 10 years:

Going from yearly to monthly adds $181; going from daily to continuous adds 56 cents. The last column is the annual percentage yield, (1 + r/n)ⁿ − 1, which folds the frequency into one yearly figure. It is the number to compare between savings accounts.

Time Beats Rate

Regular deposits compound from the month they go in, so starting earlier matters more than almost anything else. $300 a month at 7% compounded monthly:

Ten more years of deposits, $36,000 more money in, more than doubles the result. When the deposit is made in the month matters a little: $200 a month at 6% for 30 years gives $200,903.01 with deposits at the end of each month and $201,907.52 at the start, because each deposit gets one extra month of growth.

The Rule of 72, Checked

Dividing 72 by the yearly rate estimates how many years money takes to double. With yearly compounding the exact doubling time is ln 2 ÷ ln(1 + r):

The rule is within a fraction of a year between about 4% and 12%, best near 8%, and drifts at low and high rates. It works in reverse too: debt at 18% doubles in a little over four years if nothing is paid.

Withdrawals

The same arithmetic runs backwards for withdrawals. $100,000 earning 4% with $1,000 taken out every month lasts until month 122, about ten years, because the interest still covers part of each withdrawal. Enter a negative monthly amount in the calculator to see when a balance runs out.

What the Numbers Leave Out

A calculator assumes one fixed rate for the whole period. Savings rates change, investment returns vary from year to year and can be negative, and taxes, fees and inflation all reduce what the balance is worth. The SEC’s Investor.gov calculator lets you see a range of rates for this reason; it is worth running a lower rate alongside your hopeful one.

How We Checked These Numbers

Every balance here comes from the calculator’s own functions, which we compared with an independent 60-digit decimal simulation on 1,507 random cases: all 30,032 year-end balances matched to the cent, and every lump-sum case equalled the textbook formula.

Frequently Asked Questions

Published Oct 14, 2026 by Derek Giordano