The Power of Compound Interest
Albert Einstein reportedly called compound interest the "eighth wonder of the world." Unlike simple interest (calculated only on principal), compound interest earns interest on your accumulated interest — creating exponential growth over time.
Compound Interest Formula
A = P(1 + r/n)^(nt)
Where A = final amount, P = principal, r = annual rate, n = compounding periods per year, t = time in years.
Why Starting Early Matters
If you invest $10,000 at age 25 at 7% annually, it grows to ~$149,745 by age 65. The same investment made at age 45 only grows to ~$38,697. Starting 20 years earlier yields 4× more money — this is the time value of money in action.
Worked Examples: Compounding and Regular Contributions
Suppose you invest $10,000 and earn an average of 7% per year for 20 years. With interest compounded annually it grows to about $38,697; compounded monthly it grows to about $40,387. The more often interest is added, the more you earn on prior interest, though the difference between monthly and daily compounding is small.
Regular contributions have a bigger effect than frequency. If you add $200 per month for 30 years at 7%, you contribute $72,000 yourself and end with about $243,994, so roughly $171,994 comes from compound growth. Starting ten years later with the same $200 per month would leave you with far less, which is why starting early matters so much. The 7% figure is only an illustration: actual investment returns vary from year to year and are never guaranteed.
The Rule of 72 and APR vs. APY
A quick way to estimate doubling time is the Rule of 72: divide 72 by the annual return. At 7% your money doubles in about 10.3 years, and at 10% in about 7.2 years. When comparing savings accounts, look at APY (annual percentage yield), which includes compounding, rather than the stated interest rate (APR) alone. Fees and taxes also reduce your real return, so factor them in when planning.
Prepared by the ProCalcTools editorial team and last reviewed in October 2026. This page is for general information and is not financial, tax, or medical advice.