See how compound interest grows your investment over time with customizable compounding frequency.
Optional — added at the end of each month
A = P(1 + r/n)^(nt) + PMT × [(1 + i)^(12t) − 1] / iP = principal, r = annual rate, n = compounds per year, t = years, PMT = monthly contribution, and i = (1 + r/n)^(n/12) − 1, the monthly rate equivalent to your compounding frequency. At 0% interest the contributions simply add up.
APY (effective annual yield) = (1 + r/n)^n − 1.
Compound interest means you earn interest on your interest, not just the original principal. This leads to exponential rather than linear growth.
The balance after t years is A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate and n the number of times interest compounds per year. Regular contributions are added as an annuity on top. For example, $10,000 at 7% compounded monthly grows to about $20,097 in 10 years.
Savings accounts typically compound daily or monthly, while many bonds compound semi-annually. The more often interest compounds, the higher the effective annual yield (APY), although the difference between daily and monthly is small.
APR is the simple annual rate. APY includes the effect of compounding within the year, so it is higher whenever interest compounds more than once a year: 5% compounded monthly is an APY of about 5.12%.
Divide 72 by the annual interest rate to estimate how many years it takes to double your money. At 7%, money doubles in roughly 10 years (the exact figure with annual compounding is about 10.2 years).
The more frequently interest compounds, the faster your money grows. Annual compounding calculates interest once per year, while daily compounding does so 365 times. The difference becomes significant with larger balances and higher rates. A $100,000 investment at 5% earns $5,000 with annual compounding but $5,127 with daily compounding.
A 25-year-old investing $200/month at 8% return will have approximately $702,000 by age 65. A 35-year-old investing the same amount at the same rate will have only $298,000 — less than half. Those extra 10 years of compounding are worth over $400,000, despite contributing only $24,000 more in total.
Did you know?
If you invested $1,000 at 10% annual compound interest, it would grow to over $1 million in approximately 73 years — without adding a single dollar more. This demonstrates why starting to invest early is so powerful.
Compound interest has been used since ancient Babylon, but the mathematical formula was formalized by Jacob Bernoulli in 1683 while studying the problem of continuous compounding. His work led to the discovery of the mathematical constant "e" (approximately 2.71828), which is fundamental to exponential growth calculations used in finance today.
Warren Buffett earned 99% of his $100+ billion net worth after his 50th birthday, demonstrating the exponential nature of compound growth over time.
The Rule of 72 lets you quickly estimate doubling time: divide 72 by your interest rate. At 8% return, your money doubles every 9 years.
Daily compounding vs. annual compounding on a $10,000 deposit at 5% yields an extra $12.74 per year — the difference grows significantly with larger amounts.
Benjamin Franklin left $1,000 each to Boston and Philadelphia in 1790. By 1990, the funds had grown to $4.5 million and $2 million respectively through compound interest.