How Compound Interest Works (With Examples, 2026)

The formula and the idea

For a lump sum, the compound interest formula is:

A = P × (1 + r/n)^n·t

where A is the final amount, P is the starting principal, r is the annual rate, n is how many times a year it compounds, and t is the number of years. The key is the exponent: because the balance is multiplied period after period, the curve bends upward instead of rising in a straight line the way simple interest does.

A 30 year example

The real power shows up when you add money regularly and leave it alone for decades.

Worked example: $10,000 start + $300 a month, 7 percent, 30 years

Starting balance$10,000
Monthly contribution$300
Total you contribute over 30 years$118,000
Ending balance$447,156
Growth (interest on interest)$329,156

You put in 118,000 dollars. The account grew to over 447,000 dollars, and nearly 330,000 of that is growth you never deposited. That gap is compounding.

The rule of 72 and why time beats timing

The rule of 72 is a shortcut: divide 72 by your annual return to estimate the years it takes to double your money. At 7 percent, 72 divided by 7 is about 10.3 years to double, and it doubles again after that, and again. That is why starting early matters more than the exact amount. A dollar invested in your twenties has decades to double repeatedly; the same dollar invested in your fifties may double only once. Time in the market, not timing the market, is what compounding rewards.

Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is paid only on your original principal, so it grows in a straight line. Compound interest is paid on the principal plus all previously earned interest, so the balance grows faster and faster over time.

Does more frequent compounding matter much?

A little. Daily versus monthly versus yearly compounding makes a small difference at the same rate. What dominates the outcome is the rate itself and, above all, the number of years you stay invested.

How does the rule of 72 work?

Divide 72 by the annual percentage return to approximate how many years it takes your money to double. At 6 percent that is about 12 years; at 9 percent, about 8 years. It is an estimate, but a very handy one.

Can compound interest work against me?

Yes. On debt, especially credit cards, interest compounds on your balance the same way, so an unpaid balance grows faster over time. The same force that builds savings can dig a debt hole.