How Does Compound Interest Work?
Published 11/10/2025 · 2 min read · Finance calculators
Compound interest is interest calculated on both your original money and the interest already added. The formula is A = P(1 + r/n)^(nt): principal P, annual rate r, compounded n times a year for t years. $1,000 at 5% compounded yearly grows to $1,629 in 10 years — $129 more than simple interest, because each year's interest earns interest too.
Compound interest is interest earning interest. Here's the formula, a worked example, and why starting early beats saving more later.
Simple vs compound interest
Simple interest is paid only on the original amount, so $1,000 at 5% earns a flat $50 every year. Compound interest is paid on the principal plus the interest already added, so the base grows each period. That difference is small at first and dramatic over decades — it is why compounding is often called the eighth wonder of finance.
The formula, step by step
The future value is A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of times it compounds per year and t the number of years. For $1,000 at 5% compounded once a year for 10 years: 1,000 × (1 + 0.05)^10 = 1,000 × 1.6289 = $1,628.89.
Why compounding frequency matters
The more often interest is added, the sooner it starts earning more interest. The same $1,000 at 5% over 10 years reaches about $1,629 compounded yearly, but roughly $1,647 compounded monthly. The gap is modest at these numbers, yet it widens with higher rates and longer horizons — always check whether a rate is quoted yearly, monthly or daily.
Time is the real lever
Because growth builds on itself, years matter more than amounts. Saving $100 a month from age 25 to 65 at 6% ends near $200,000; starting the same $100 a month at 35 ends closer to $100,000 — half, for ten fewer years. The earlier you start, the more of the final total is interest rather than your own contributions.
Worked with our own calculator
Compound interest calculator
Given
- Initial amount
- $10,000.00
- Monthly contribution
- $200.00
- Annual rate (%)
- 5
- Duration (years)
- 15
Result
- Final balance
- $74,594.83
- Total invested
- $46,000.00
- Interest earned
- $28,594.83
These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.
Run it on your own figures →Frequently asked questions
- What's the difference between APR and APY?
- APR is the nominal yearly rate and ignores compounding; APY (or effective rate) includes it, so APY is the true annual return. At 12% compounded monthly the APY is about 12.68%.
- How often is interest usually compounded?
- Savings accounts often compound monthly or daily, while bonds may pay annually or semi-annually. Always check the terms, since the frequency changes the final amount.
- Does compound interest work against me on debt?
- Yes. Credit card balances compound, so unpaid interest itself starts accruing interest — which is why carrying a balance gets expensive fast.
Articles you may find interesting
All guides →Related tools
Sources
Spotted a mistake in this article?