How Compound Interest Works: Formula and Examples
Learn compound growth, deposit timing, compounding frequency and inflation effects.
Compound interest means returns can accrue on both the starting principal and interest credited earlier. Growth depends on the stated rate, the compounding convention, contribution timing, and how long the money remains invested.
Compound interest formula
For an initial principal P, nominal annual rate r, compounding periods per year n, and time in years t:
A = P × (1 + r/n)^(n×t)
For example, $5,000 earning 6% nominal annually compounded monthly for five years becomes approximately $6,744 before tax and fees. This is an illustration, not a promise of future investment returns.
Compounding frequency
Interest might be compounded yearly, quarterly, monthly, or daily. Using the same nominal annual rate, more frequent compounding slightly increases the effective annual yield. The effective annual rate is (1 + r/n)^n − 1. Always compare products using compatible definitions of annual yield rather than assuming advertised percentages are identical.
Adding recurring deposits
Monthly savings can grow alongside principal, but the formula changes. Deposits at the beginning of each month have more time to earn interest than deposits at month-end. Check which assumption your calculator uses before comparing a projection with another tool.
Nominal growth versus purchasing power
Inflation can reduce how much a future balance will buy. A balance projected to reach $100,000 in 20 years is not equivalent to $100,000 in today’s purchasing power. To estimate today’s equivalent at a steady annual inflation rate i, divide the future value by (1+i)^20.
Important limitations
Real-world investment returns fluctuate; they do not arrive as a guaranteed constant rate. Fees, taxes, market losses, and contribution limits may materially change the outcome. Bank deposit interest conventions can also differ from model assumptions. Compare several return scenarios rather than treating a single output as certain.
Frequently misunderstood concepts
Is compound interest always better than simple interest? At the same positive rate and holding period, compounding generally increases the ending amount, assuming no other differences.
Can interest compound with no contributions? Yes. Compounding applies to an existing principal even when no new money is added.
Is a calculator result a guaranteed investment return? No. It is a projection based on the assumptions supplied.