Compound Interest Formula Explained, With Real Examples

Compound interest is interest earned on interest. In the first year you earn a return on the money you put in; in the second year you also earn a return on the first year's interest, and so on. Over long periods, that snowball effect does most of the work. Below is the formula, what each letter means and several worked examples you can check yourself.

Simple vs. compound interest

With simple interest, you only earn on the original amount. $10,000 at 5% simple interest earns $500 every year, so after 10 years you have $15,000.

With compound interest, each year's interest is added to the balance and earns interest too. The same $10,000 at 5% compounded once a year grows to $16,288.95 after 10 years. The extra $1,288.95 is interest on interest.

The compound interest formula

A = P × (1 + r/n)^(n × t)

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

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

Compounded annually: A = 10,000 × (1 + 0.05/1)^(1 × 10) = 10,000 × 1.05^10 = $16,288.95.

Now see what happens when interest is added more often:

Compounding	n	Balance after 10 years
Annually	1	$16,288.95
Monthly	12	$16,470.09
Daily	365	$16,486.65
Continuously	∞	$16,487.21

More frequent compounding helps, but with diminishing returns: going from yearly to monthly adds about $181, while going from monthly to daily adds only about $17. The rate and the time matter far more than the compounding frequency.

APR vs. APY

This is why banks quote two numbers. The APR (annual percentage rate) is the nominal rate, the "r" in the formula. The APY (annual percentage yield) is what you actually earn in a year once compounding is included. A 5% APR compounded monthly equals an APY of about 5.12%. When comparing savings accounts, compare APYs.

Adding monthly contributions

Most people don't invest a lump sum once; they add money every month. The future value of regular contributions is:

FV = PMT × [((1 + i)^N − 1) ÷ i]

where PMT is the monthly deposit, i is the monthly rate (annual rate ÷ 12) and N is the number of months.

Example: $200 a month at 6% a year for 20 years. i = 0.06 ÷ 12 = 0.005 and N = 240.

• You deposit 200 × 240 = $48,000 in total.
• The account grows to about $92,408.
• More than $44,000 of that is interest.

Start the same plan 10 years later and you end up with far less, not half as much. That is the real lesson of compounding: time in the market beats almost every other variable.

The Rule of 72

To estimate how long it takes to double your money, divide 72 by the annual rate:

• At 6%: 72 ÷ 6 = 12 years (the exact answer is 11.9)
• At 8%: 72 ÷ 8 = 9 years
• At 3%: 72 ÷ 3 = 24 years

It also works in reverse for debt and inflation. At 3% inflation, prices double in roughly 24 years.

Compound interest works against you on debt

Credit cards often charge 20% or more APR, compounded daily. An unpaid balance of $3,000 at 22% grows by more than $730 in a year if you make no payments. The same math that builds savings builds debt, which is why paying off high-interest balances is usually the best "investment" available.

How to use the calculator

1. Enter the starting amount and, if you want, a monthly contribution.
2. Enter the annual rate and choose the compounding frequency.
3. Enter the period in years or months.
4. Compare the result with simple interest to see how much compounding adds.

Remember: real investments don't grow at a fixed rate every year, and taxes and fees reduce returns. Use the calculator for planning and comparison, not as a promise of future results.

Frequently asked questions

What is the formula for compound interest?

A = P(1 + r/n)^(nt), where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years.

Is monthly or daily compounding better?

Daily compounding pays slightly more, but the difference is small. On $10,000 at 5% for 10 years, daily compounding beats monthly by about $17.

How long does it take to double money at 7%?

Using the Rule of 72, about 72 ÷ 7 ≈ 10.3 years.

What is the difference between APR and APY?

APR is the nominal annual rate. APY includes the effect of compounding during the year, so it is always equal to or higher than the APR.

Informational content only. For legal, financial or health decisions, consult a qualified professional.