Compound interest explained, with real examples

Compound interest is interest earned on interest. Each period’s interest is added to your balance, so the next period’s interest is calculated on a bigger number. $10,000 earning an example 5% a year, compounded annually, grows to $16,288.95 in 10 years and $43,219.42 in 30 years, against $15,000 and $25,000 with simple interest. The formula is A = P(1 + r/n)^(nt).

Below we unpack the formula, show why time matters more than anything else, clear up APY versus APR, and give you the Rule of 72 for quick mental math. Every figure comes from the same code as our compound interest calculator, so you can reproduce it there.

Simple vs compound interest, year by year

Investor.gov gives the smallest possible example: $100 earning 5% a year becomes $105 after one year and $110.25 after two. The extra 25 cents in year two is interest on the first year’s $5 of interest. Scale that up and let it run:

For the first few years the two barely differ. Then the gap widens every year, because each year’s interest is bigger than the last. That curve is the whole story of compounding: it rewards time more than anything else.

The compound interest formula

A = P × (1 + r/n)^(n × t)

• A: the final balance
• P: the starting amount (principal)
• r: the annual interest rate as a decimal (5% = 0.05)
• n: compounding periods per year (1 annually, 12 monthly, 365 daily)
• t: the number of years

If you also add a fixed amount C at the end of every month, those deposits grow to C × ((1 + i)^m − 1) ÷ i, where i is the monthly rate and m is the number of deposits. When the compounding schedule is not monthly, our calculator first converts the rate to the equivalent monthly rate, i = (1 + r/n)^(n/12) − 1, so both parts grow consistently.

Worked example 1: $10,000 at 5%, compounded monthly, for 10 years

1. Rate per period: r ÷ n = 0.05 ÷ 12 = 0.0041666667
2. Number of periods: n × t = 12 × 10 = 120
3. Growth factor: (1 + 0.05/12)^120 = 1.6470095
4. Final balance: $10,000 × 1.6470095 = $16,470.09
5. Interest earned: $16,470.09 − $10,000 = $6,470.09

That is $181.14 more than the same rate compounded once a year.

Does compounding frequency matter?

More frequent compounding helps, but with sharply diminishing returns: daily beats monthly by just $16.56 over a decade. A slightly higher rate, or a few more years, is worth far more than a better compounding schedule.

APY vs APR: which number to compare

The “effective annual rate” column above has a name on US bank disclosures. Under the Truth in Savings Act and its Regulation DD, banks must quote deposit accounts with an annual percentage yield (APY), which reflects both the interest rate and how often it compounds over a 365-day year. A 4.00% rate compounded daily is a 4.08% APY; compounded monthly it is 4.07%. Compare savings accounts and CDs by APY.

Borrowing is quoted as an annual percentage rate (APR), which does not include compounding. On a mortgage, the CFPB explains, the APR also folds in points, broker fees and other charges, so it is usually higher than the interest rate. On a credit card, the CFPB explains that issuers typically divide the APR by 365 (or 360) to get a daily periodic rate and add each day’s interest to the balance, so interest compounds daily. A 24% APR compounded daily works out to an effective 27.11% a year on a balance you do not pay down.

Worked example 2: starting at 25 vs starting at 35

Three savers put $200 into an investment at the end of each month and stop at age 65. We assume an illustrative 7% average annual return compounded monthly. Real investment returns are not guaranteed and vary from year to year, so treat this as a picture of the math, not a forecast.

The saver who deposits for only ten years and then stops ends up with more than the saver who deposits for thirty years but starts a decade later. To match the early starter, the 35-year-old would need to save $430.31 a month, more than twice as much. If saving more feels impossible, even raising contributions by a small percentage each time your pay goes up adds up; our percentages guide shows how to work out a raise.

The Rule of 72

To estimate how long money takes to double, divide 72 by the annual rate. Investor.gov gives the example of a 9% return doubling in about 8 years. The exact answer, with annual compounding, is ln 2 ÷ ln(1 + r):

It works on debt and inflation too. At 24% APR, an unpaid card balance doubles in about 72 ÷ 24 = 3 years (2.89 years with daily compounding).

When compounding works against you

Leave $5,000 on a card at 24% APR, compounded daily, for a year with no payments and no new charges, and it grows to $6,355.74: $1,355.74 of interest. Real statements also involve minimum payments and possibly fees, but the direction is the same. Paying off high-rate debt is often the best guaranteed “return” available.

Installment loans work differently when you pay on schedule: each payment covers that month’s interest, so interest does not pile up on itself. But on a long loan most of the early payment is interest. On a $300,000, 30-year mortgage at an example 6.5%, the first $1,896.20 payment is $1,625.00 interest and just $271.20 principal. See how much house you can afford and why longer car loans cost more, or model any loan in the loan calculator.

Don’t forget inflation

Growth only matters in what it can buy. Inflation is tracked in the US by the Bureau of Labor Statistics’ Consumer Price Index. If savings earn 4% while prices rise 3% (both illustrative), your purchasing power grows by about 1.04 ÷ 1.03 − 1 = 0.97% a year, not 4%.

Putting compounding to work

• Start early and automate. Time is the biggest lever, as example 2 shows.
• Compare by APY for savings and by APR for loans, and watch fees, which compound against you too.
• Know what is insured. FDIC deposit insurance covers deposits up to $250,000 per depositor, per insured bank, for each account ownership category. Stocks, bonds, mutual funds and crypto assets are not FDIC-insured, even if you buy them through a bank, and can lose value.
• Pay down high-rate debt first, since it compounds faster than most savings grow.

This guide explains the math; it is not financial or investment advice. Try your own deposit, rate and timeline in the compound interest calculator, and use the percentage calculator to turn any two balances into a percentage change.