What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — which only earns returns on the original amount — compound interest creates a snowball effect where your earnings generate their own earnings.
Albert Einstein allegedly called compound interest the 'eighth wonder of the world.' Whether or not he actually said it, the math is genuinely remarkable. A $10,000 investment at 8% annual return becomes $21,589 after 10 years with compound interest — but only $18,000 with simple interest. Over 30 years, the gap grows to $100,627 (compound) vs. $34,000 (simple). The longer the time horizon, the more dramatic the difference.
The key variables that determine compound growth are: principal (starting amount), rate of return, compounding frequency (how often interest is calculated and added), and time. Of these, time is the most powerful — which is why starting to invest early, even with small amounts, beats starting late with large amounts.
The Compound Interest Formula
The standard compound interest formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is time in years.
For $10,000 invested at 7% compounded monthly for 20 years: A = 10,000 × (1 + 0.07/12)^(12×20) = 10,000 × (1.005833)^240 = $40,064.
Compounding frequency matters, but less than people think. The difference between annual and daily compounding on $10,000 at 7% over 10 years is only about $190. The real variable that matters is whether the stated rate is APR (annual percentage rate — what banks advertise) or APY (annual percentage yield — what you actually earn accounting for compounding). A savings account advertising 5% APR compounded daily has an APY of 5.127%. Always compare APYs when shopping for savings accounts.
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The Rule of 72: Mental Math for Doubling Time
The Rule of 72 is the fastest mental shortcut for compound interest: divide 72 by your annual interest rate to estimate how many years it takes for an investment to double.
At 6% return: 72/6 = 12 years to double. At 8%: 72/8 = 9 years. At 12%: 72/12 = 6 years. This simple rule is accurate to within a year for rates between 4–16%.
The reverse also works for inflation: at 3% inflation, your purchasing power halves in 72/3 = 24 years. This is why a retirement nest egg needs to earn returns above inflation — a $1 million portfolio in 2024 will have the purchasing power of only $552,000 in 2048 if inflation averages 3%.
The Rule of 72 is also useful for evaluating credit card debt. At 20% APR: 72/20 = 3.6 years for debt to double if you make no payments. That's why the math of compound interest works against you just as powerfully when you're the borrower.
Regular Contributions: The Missing Variable
Most compound interest calculators — including the ones on Investor.gov and many bank websites — show growth of a lump sum. But real wealth building happens through regular contributions to a growing balance.
Adding $500/month to a $10,000 initial investment at 8% for 30 years produces $745,179 — more than five times the $100,627 you'd get from the lump sum alone. The monthly contributions of $180,000 total generate $554,552 in compound returns.
This is the math behind retirement accounts. The Roth IRA contribution limit ($7,000/year in 2024) invested from age 25 to 65 at 7% average return yields $1,497,446 tax-free. The same contributions starting at 35 yield only $756,560 — half as much, despite only losing 10 years. This 10-year head start doubles your ending balance, which is why personal finance advisors are so emphatic about starting early.