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How Compound Interest Works: The Math Behind Growing Your Money

2026-10-21 · compound interest, savings, investing, finance

Compound interest is often called the eighth wonder of the world — and for good reason. Unlike simple interest, which only ever applies to your original principal, compound interest lets you earn interest on your interest. Over time, that snowball effect can turn modest, regular savings into serious wealth.

How compound interest works

Imagine you invest $1,000 at a 7% annual return, compounded yearly. After year one you have $1,070. In year two, you earn 7% not on $1,000 but on $1,070 — that's $74.90, bringing your total to $1,144.90. Each year the base grows, so the interest earned grows too.

The formula is simple:

A = P × (1 + r/n)nt

Where P is your starting principal, r is the annual interest rate, n is how many times interest compounds per year, and t is the number of years.

Why compounding frequency matters

Money compounded monthly grows slightly faster than money compounded yearly at the same rate, because each month's interest starts earning sooner. Daily compounding pushes it a little further still. The differences look small in year one — but over 20 or 30 years they become very real money.

Try it yourself

Use our free Compound Interest Calculator to see exactly how your savings could grow. Enter your principal, rate, compounding frequency and time horizon, and watch the snowball in action.

Remember: these are estimates for education, not financial advice. Actual investment returns vary.