How Compound Interest Works (and Why Time Matters)
Compound interest is the mechanism behind long-term wealth: interest earned on interest. Understanding it — and especially the role of time — changes how you think about every saving and investing decision.
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What Compounding Actually Is
Simple interest pays on the original amount only. Compound interest pays on the original amount plus all previously earned interest. Each period's interest is added to the pot, so the next period earns on a bigger pot — growth accelerates.
Example: $1,000 at 10% simple interest earns $100 every year, forever. At compound interest, year 1 earns $100 (balance $1,100), year 2 earns $110 (balance $1,210), year 3 earns $121 (balance $1,331). The yearly gain grows because the base grows.
The Formula
A is the future value, P the principal, r the annual interest rate as a decimal, n the compounding frequency per year and t the years. For annual compounding (n = 1) this simplifies to A = P(1 + r)^t.
Regular Contributions Change Everything
Most people do not invest one lump sum — they contribute monthly. Each contribution is a separate compound-interest calculation that keeps growing. The full picture:
At 7% annual growth, $300/month over 30 years grows to roughly $365,000 — with only $108,000 of contributions. The other $257,000 is compounding doing its work.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate. At 6%: 72 ÷ 6 = 12 years. At 9%: 8 years. It is an approximation, accurate to within a year for typical rates — and a powerful way to think about the cost of delay.
Why Starting Early Beats Investing More
The person who invests $200/month from age 25 to 35 (12 years, $24,000 total) then stops, beats the person who invests $200/month from 35 to 65 (30 years, $72,000 total) — if both earn 7%. The early money simply has decades more time to compound. The calculator on this page makes this concrete: try both scenarios and compare the final balances.
Article FAQ
What is the compound interest formula?
A = P(1 + r/n)^(nt), where P is principal, r the annual rate, n compounding periods per year and t the years.
How long does money take to double?
Use the rule of 72: divide 72 by the annual rate. At 7% it takes about 10.3 years.
Does compounding frequency matter?
Slightly — more frequent compounding earns a little more at the same nominal rate. Daily vs annual is a small difference over one year but grows over decades.