The Formula and What It Means
Compound interest is calculated with this formula:
A = P(1 + r/n)^(nt)
Where:
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (decimal: 7% = 0.07)
- n = number of times interest compounds per year
- t = years
The key difference from simple interest: with compound interest, you earn interest on your interest. Each period, the interest is added to your principal, making the next period's interest calculation larger.
The Rule of 72
The Rule of 72 is a quick mental math shortcut: 72 ÷ annual rate = years to double your money.
- At 4% (high-yield savings): 72 ÷ 4 = 18 years to double
- At 7% (stock market average): 72 ÷ 7 ≈ 10 years to double
- At 10% (optimistic stock return): 72 ÷ 10 = 7.2 years to double
- At 24% (credit card): 72 ÷ 24 = 3 years to DOUBLE what you owe
The Power Over Time: Investment Example
$10,000 invested at a 7% average annual return:
| Years | Value | Total Gain |
|---|---|---|
| 10 | $19,672 | $9,672 |
| 20 | $38,697 | $28,697 |
| 30 | $76,123 | $66,123 |
| 40 | $149,745 | $139,745 |
$10,000 turns into nearly $150,000 over 40 years without adding a single dollar. The money in the final decade grew more ($73,000) than in the entire first 30 years combined ($66,000). This is exponential growth in action.
The Destruction of Debt: Credit Card Example
The same math works against you with debt. A $5,000 credit card balance at 24% APR, if you only pay the minimum (~$100/month):
- You'll pay for approximately 8–9 years
- You'll pay roughly $9,000–$10,000 total — almost double the original balance
The card issuer is compounding daily (n=365). At 24% APR with daily compounding, $1 becomes $1.271 after one year. On a $5,000 balance, that's $1,355 in interest in year one alone.
Why Starting Early Matters More Than Saving More
The most important variable in the compound interest formula is time — not the amount invested. Consider:
- Alice invests $5,000/year from age 25–35 (10 years = $50,000 total), then stops completely
- Bob invests $5,000/year from age 35–65 (30 years = $150,000 total)
At age 65 with 7% returns: Alice has ~$602,000; Bob has ~$472,000. Alice invested 1/3 as much money but has 28% more — solely because of those 10 extra years of compounding. Starting 10 years earlier was worth more than tripling the total investment.
Compound Frequency: Does It Matter?
Compounding more frequently (daily vs. annual) does produce slightly higher returns, but the difference is smaller than most people expect at typical rates:
- $10,000 at 7% for 10 years, compounded annually: $19,672
- $10,000 at 7% for 10 years, compounded daily: $20,136
The difference of $464 matters less than you'd think — which is good news, because it means your exact compounding frequency is less important than your rate, your time horizon, and your consistency. Use our CalcPeek financial calculators to model compound interest for any scenario.