What Is Compound Interest?
Compound interest is interest calculated on both your original principal AND the interest you have already earned. It is often called "interest on interest" and it is the reason Albert Einstein allegedly called it "the eighth wonder of the world."
Simple Interest vs. Compound Interest
Simple interest example: You invest $10,000 at 10% simple interest for 5 years. You earn $1,000/year = $5,000 total. Ending balance: $15,000.
Compound interest example: You invest $10,000 at 10% compound interest for 5 years.
- Year 1: $10,000 × 1.10 = $11,000
- Year 2: $11,000 × 1.10 = $12,100
- Year 3: $12,100 × 1.10 = $13,310
- Year 4: $13,310 × 1.10 = $14,641
- Year 5: $14,641 × 1.10 = $16,105
Ending balance: $16,105 — that is $1,105 more than simple interest, just from compounding!
Calculate your own growth with our free compound interest calculator.
How Compounding Frequency Affects Returns
The same annual rate compounded more frequently earns slightly more each year. Here is $10,000 at 10% for 10 years under different compounding frequencies:
| Compounding | 10-Year Balance | Effective Annual Rate | |---|---|---| | Annual | $25,937 | 10.000% | | Monthly | $27,070 | 10.471% | | Daily | $27,179 | 10.516% | | Continuously | $27,183 | 10.517% |
The difference between annual and daily compounding is about $1,242 on $10,000 over 10 years — meaningful, but not as dramatic as the difference between early investing vs. waiting.
The Power of Starting Early: A Compelling Example
Investor A invests $5,000/year from age 25 to 35 (10 years), then stops. Total invested: $50,000.
Investor B invests $5,000/year from age 35 to 65 (30 years). Total invested: $150,000.
Assuming 8% annual return, at age 65:
- Investor A: $602,070
- Investor B: $566,416
Investor A wins — with $100,000 less invested — simply by starting 10 years earlier. Time in the market beats timing the market.
The Rule of 72
A mental shortcut: divide 72 by your annual return rate to find how many years it takes to double your money.
- At 6%: 72 ÷ 6 = 12 years to double
- At 8%: 72 ÷ 8 = 9 years to double
- At 10%: 72 ÷ 10 = 7.2 years to double
- At 12%: 72 ÷ 12 = 6 years to double
Compound Interest in Real Life
- Savings accounts and CDs: Low rates (0.5–5%) with monthly compounding
- Index funds and ETFs: Historically 7–10% annual returns, compounding over decades
- Credit card debt: Compound interest works against you — 20–30% APR compounding monthly is devastating
- Mortgages: Amortized loans — early payments are mostly interest, later payments are mostly principal
FAQ
What is APY vs APR?
APR (Annual Percentage Rate) is the stated rate. APY (Annual Percentage Yield) accounts for compounding and shows the actual return you earn in a year. A 10% APR compounding monthly has an APY of 10.47%.
How do I calculate compound interest manually?
Formula: A = P(1 + r/n)^(nt) where P = principal, r = annual rate (decimal), n = compounds per year, t = years. Or use our free calculator.
Does compound interest work the same for debt?
Yes, and it is worse. On a $5,000 credit card balance at 24% APR compounded daily, if you make only minimum payments, you will pay over $10,000 in interest before it is paid off.