Compound Interest: The Eighth Wonder of the World
Einstein allegedly called compound interest the eighth wonder of the world. Learn how it works and how to make it work for you.
The Compound Interest Formula
Compound interest is calculated using this formula:
A = P(1 + r/n)nt
- A = Final amount (principal + interest)
- P = Principal (initial investment)
- r = Annual interest rate (as a decimal)
- n = Number of times interest is compounded per year
- t = Number of years
Simple vs Compound Interest
Simple interest is calculated only on the original principal: A = P(1 + rt). For example, $10,000 at 5% simple interest for 10 years earns $5,000 in interest, giving you $15,000 total.
Compound interest earns interest on previously earned interest. The same $10,000 at 5% compounded annually for 10 years grows to $16,289 — that is $1,289 more, just from compounding.
Compounding Frequency Matters
The more frequently interest compounds, the more you earn. With $10,000 at 5% for 10 years:
- Annually: $16,288.95
- Monthly: $16,470.09
- Daily: $16,486.65
The difference between annual and daily compounding is modest, but over larger amounts and longer periods, it becomes significant.
The Rule of 72
Want a quick estimate of how long it takes to double your money? Divide 72 by your interest rate. At 6% interest, your money doubles in approximately 72 / 6 = 12 years. At 8%, it takes about 9 years. This rule is a handy mental shortcut for evaluating investments without a calculator.
Ready to calculate? Try the Compound Interest Calculator →