Compound interest explained

What is compound interest?

Investor.gov, the investor education site of the US Securities and Exchange Commission (SEC), sums it up in one line: “Compound interest is the interest you earn on interest.”

Compare the two ways interest can be paid:

• Simple interest is paid only on the original amount (the principal). $1,000 at 5% simple interest earns $50 every year, forever.
• Compound interest is added to the balance, so next year’s interest is calculated on a bigger number. The $50 earned in year one earns interest itself in year two.

Investor.gov’s own example: “if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.” The extra 25 cents is interest on the first year’s $5. It looks tiny — but it keeps growing.

What is the compound interest formula?

The standard formula for a single deposit is:

A = P × (1 + r ÷ n)^{n × t}

• A = amount at the end
• P = principal (what you start with)
• r = yearly interest rate as a decimal (5% = 0.05)
• n = how many times a year interest is compounded (1 = yearly, 12 = monthly, 365 = daily)
• t = number of years

Checking Investor.gov’s example with yearly compounding: 100 × (1 + 0.05)¹⁰ = $162.89 after 10 years (“more than $162”, as Investor.gov says) and 100 × 1.05²⁵ = $338.64 after 25 years (“almost $340”).

How much difference does compounding make over time?

The table below is illustrative: $1,000 at a fixed 5% a year, compounded yearly, with no withdrawals. Real savings rates change and investment returns are not fixed.

How it is worked out: simple = 1,000 + (50 × years). Compound = 1,000 × 1.05^years; for 30 years, 1.05³⁰ = 4.32194, so $4,321.94. In the first 10 years the gap is under $130; by year 30 it is more than $1,800. Time does most of the work.

What happens if you add money every month?

Regular deposits compound too. Investor.gov’s free compound interest calculator asks for exactly these inputs: an initial investment, a monthly contribution, the length of time in years, an estimated interest rate, a range of rates to compare, and the compound frequency — “Times per year that interest will be compounded.”

Illustrative example: $100 a month for 10 years at 5%, compounded monthly. The future value of regular payments is:

FV = payment × ((1 + r ÷ 12)^months − 1) ÷ (r ÷ 12)

100 × ((1 + 0.05 ÷ 12)¹²⁰ − 1) ÷ (0.05 ÷ 12) = $15,528.23, from $12,000 paid in. The difference, $3,528.23, is compounded interest. A similar idea — putting in a fixed amount on a schedule — is behind dollar-cost averaging, though investments do not earn a fixed rate.

How does compounding frequency change the result?

The more often interest is added, the faster the balance grows — slightly. For a 5.00% rate on $1,000 over one year (illustrative):

• Yearly: 1,000 × 1.05 = $1,050.00
• Monthly: 1,000 × (1 + 0.05 ÷ 12)¹² = $1,051.16
• Daily: 1,000 × (1 + 0.05 ÷ 365)³⁶⁵ = $1,051.27

This is why US savings accounts disclose an annual percentage yield (APY). Under the CFPB’s Truth in Savings rule, the APY reflects “the interest rate and the frequency of compounding”, while the plain interest rate “does not reflect compounding”. More in how interest rates work.

What is the Rule of 72?

Investor.gov describes a shortcut for estimating how long money takes to double: “Simply divide the number 72 by your investment's expected rate of return (interest rate).” Its example: at 9%, an investment doubles about every 8 years (72 ÷ 9 = 8).

Checking the arithmetic: 1.09⁸ = 1.993, so close to double. At 6%, 72 ÷ 6 = 12 years, and 1.06¹² = 2.012. It is an approximation, not an exact answer, and it only applies if the rate actually holds — something no investment can promise.

What are the risks and limits of compound interest?

• It works against you on debt. Debt follows the same maths. Illustrative, hypothetical rate: $1,000 at 20% APR compounded monthly with no payments grows to 1,000 × (1 + 0.20 ÷ 12)¹² = $1,219.39 in a year. Investor.gov warns that unpaid card interest “may greatly exceed the amount you could earn on your savings or investments.”
• Inflation eats into it. A 5% return with 3% inflation is roughly a 2% real gain (exactly 1.05 ÷ 1.03 − 1 = 1.94%). See what inflation is.
• Returns are not fixed. Calculators assume a steady rate. Investor.gov notes that “All investments involve some degree of risk.” Investment values can fall, and losses compound too.
• Beware “compounding” sales pitches. Promises of guaranteed or very high returns are a red flag that US regulators list for investment scams, however impressive the compounding chart looks. Learn the red flags of crypto scams.

The examples on this page are arithmetic illustrations, not forecasts or recommendations.