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 calculates interest on the original principal), compound interest causes your balance to grow exponentially — earning "interest on interest." Einstein reportedly called it the "eighth wonder of the world."
A = P(1 + r/n)^(nt)
Where: A = final amount, P = principal, r = annual interest rate (decimal), n = compounding frequency per year, t = time in years.
Compounding Frequency Comparison
On $10,000 at 10% annual rate for 10 years, compounding frequency significantly affects the final amount:
Annual (n=1): $25,937
Quarterly (n=4): $26,851
Monthly (n=12): $27,070
Daily (n=365): $27,179
More frequent compounding yields more, but the difference between monthly and daily is small. Annual vs monthly compounding has much greater impact. Most savings accounts and mortgages compound monthly.
The Rule of 72
A quick mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double your money at compound interest.
At 6% return: 72 ÷ 6 = 12 years to double
At 8% return: 72 ÷ 8 = 9 years to double
At 12% return: 72 ÷ 12 = 6 years to double
At 2% (savings account): 72 ÷ 2 = 36 years to double
This rule helps quickly compare investment options and understand the impact of inflation on purchasing power.
Compound Interest in Practice
- 401k/IRA investing: Long-term retirement accounts benefit most from compounding. Starting at 25 vs 35 can mean 2x the final balance due to an extra 10 years of compounding
- Stock market (S&P 500): Historical average ~10%/year nominal, ~7% real (inflation-adjusted). $10,000 invested at 25 grows to ~$280,000 at 65 at 9% compound growth
- High-interest debt: Compound interest works against you with credit cards (~20–30% APR). A $5,000 balance at 24% APR with minimum payments can take 15+ years to pay off, costing over $9,000 in interest
- HYSA (High-Yield Savings): Online savings accounts offering 4–5% APY (2024) compound daily or monthly — significantly better than traditional banks offering 0.01%
Frequently Asked Questions
What's the difference between APR and APY?
APR (Annual Percentage Rate) is the nominal interest rate without compounding. APY (Annual Percentage Yield) accounts for compounding and reflects the true annual return. A savings account with 5% APR compounded monthly has an APY of approximately 5.116% — this is what you actually earn. When comparing savings accounts, compare APY, not APR.
How does inflation affect compound interest?
To find your real (inflation-adjusted) return, use the Fisher equation: Real rate ≈ Nominal rate – Inflation rate. If your investment earns 8% but inflation is 3%, your real purchasing power grows at ~5%. A 2% savings account with 3% inflation is actually losing purchasing power. Always factor inflation into long-term projections.
When does compound interest hurt rather than help?
Compound interest works against you with debt — credit cards, personal loans, and student loans all compound. Credit card balances at 24% APR compound daily, causing debt to grow rapidly if only minimum payments are made. The same mathematical force that builds wealth with investments destroys wealth with high-interest debt. Paying off 20%+ debt is the guaranteed best "investment."