Compound interest is interest earned on both your original principal and the accumulated interest from previous periods. Unlike simple interest, which only calculates on the principal, compound interest creates exponential growth over time.
Albert Einstein reportedly called compound interest the eighth wonder of the world. Whether or not he actually said it, the math backs up the sentiment — consistent investing with compound growth beats nearly every other wealth-building strategy.
The formula for compound interest is: A = P(1 + r/n)^(nt) Where: - A = final amount - P = principal (starting amount) - r = annual interest rate (decimal) - n = compounding frequency per year - t = number of years
For monthly compounding (most common): n = 12. For daily compounding: n = 365. The more frequent the compounding, the faster your money grows — though the difference between monthly and daily is typically small.
The Rule of 72 is a quick mental math trick: divide 72 by your interest rate to estimate how many years it takes to double your money. - At 6% interest: 72 / 6 = 12 years to double - At 8% interest: 72 / 8 = 9 years to double - At 10% interest: 72 / 10 = 7.2 years to double
This approximation works because of the mathematical properties of logarithms and compound growth. It is remarkably accurate for rates between 4% and 15%.
Imagine you invest $10,000 at age 25 with an 7% annual return, compounded monthly, and add $500 per month: - Age 35: $114,000 - Age 45: $317,000 - Age 55: $709,000 - Age 65: $1,450,000 Total contributions: $250,000. Compound interest contributed: $1,200,000.
The key insight: starting early matters more than contributing large amounts. A person who invests $300/month from age 25 ends up with more than someone who invests $600/month from age 35.
Our free Savings Calculator shows compound interest in action. Enter your starting amount, monthly contribution, interest rate, and time horizon to see how much compound growth contributes to your final balance.