Compound interest is the process of earning interest on both the initial principal and previously accumulated interest. The formula A = P(1 + r/n)^(nt) calculates the future value, where P is principal, r is annual rate, n is compounding frequency, and t is time in years. Albert Einstein allegedly called compound interest 'the eighth wonder of the world' — a $10,000 investment at 7% annual return grows to $76,123 in 30 years without any additional contributions.
What is Compound Interest?
Compound interest is interest earned on both your original investment and the interest already accumulated. It's what turns small, consistent contributions into significant wealth over time. The key factor is time — the longer your money compounds, the more dramatic the growth becomes. This is why starting early, even with small amounts, matters more than investing large sums later.
The formula: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)], where P is the principal, r is the annual rate, n is the compound frequency, t is time in years, and PMT is the periodic contribution.
What is the Rule of 72?
A quick mental shortcut: divide 72 by your annual return rate to estimate how many years it takes to double your money. At 6%, your money doubles in ~12 years. At 8%, in ~9 years. At 12%, in just 6 years. This rule works best for rates between 2% and 15%.
How much do you need for FIRE (Financial Independence)?
FIRE (Financial Independence, Retire Early) uses the 4% rule from the Trinity Study: you can safely withdraw 4% of your portfolio per year without running out of money over a 30-year retirement. This means your FIRE target is 25× your annual expenses. Spend $40,000/year? You need $1,000,000. Spend $60,000/year? You need $1,500,000. Use this calculator to see how long it takes to reach your number.
What do the variables in the compound interest formula mean?
| Variable | Meaning |
|---|---|
| P | Principal (initial investment) |
| r | Annual interest rate (as decimal) |
| n | Compound frequency per year (12 = monthly, 4 = quarterly, 1 = annually) |
| t | Time in years |
| PMT | Periodic contribution (monthly contribution × 12/n) |
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