Personal Finance
Compound Interest
Interest on interest — exponential growth in savings and debt
Compound interest is interest calculated on the principal plus accumulated interest. Result: exponential growth. Formula: A = P(1 + r/n)^(nt), where P principal, r rate, n compounding frequency, t time. "Eighth wonder of the world" attributed to Einstein. Power: $1000 at 5% annual compound interest for 30 years = $4322. Same simple interest: $2500. Difference: $1822. Critical for: retirement planning, debt accumulation, investment growth. Magic of long-term: small early investments grow enormously. Conversely: compound interest on debt is dangerous.
- FormulaA = P(1 + r/n)^(nt)
- Difference from simpleInterest on accumulated interest
- 30 years at 5%$1000 → $4322 (compound) vs $2500 (simple)
- Time valueEarlier investment grows much more
- Rule of 7272 / rate = years to double
- Cited byOften Einstein (probably apocryphal)
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Why compound interest matters
- Personal finance. Savings and investing.
- Retirement planning. Long-term growth.
- Debt management. Credit card debt.
- Investment. Returns over time.
- Education. Foundation of finance.
- Mortgage decisions. Total cost.
- Business finance. Capital growth.
Common misconceptions
- Linear growth. Exponential.
- Difference small. Massive over decades.
- Same as simple interest. Different mechanics.
- Just for savings. Debt too — opposite direction.
- Late saving works. Time matters more than amount.
- Need huge contributions. Small + early outperforms large + late.
Frequently asked questions
What's compound interest?
Interest calculated on principal + accumulated interest. Year 1: interest on principal. Year 2: interest on principal + Year 1 interest. Year 3: interest on principal + accumulated. Result: exponential growth (vs linear for simple interest). Formula. A = P(1 + r/n)^(nt). P principal, r rate, n compounding frequency per year, t years.
What's the difference from simple interest?
Simple: interest only on principal. Linear growth. $1000 at 5% simple: $50/year forever (until paid off). Total over 30 years: $1500 interest = $2500. Compound: interest on principal + accumulated. Exponential growth. $1000 at 5% compound: $4322 after 30 years. Difference: $1822 — significant!
What's the Rule of 72?
Quick approximation. 72 / interest rate (in %) = years to double. 5% rate: 72/5 = 14.4 years to double. 10% rate: 7.2 years. 3% rate: 24 years. Useful: estimating doubling time without calculator. Approximate but close. Works because of natural log of 2 ≈ 0.693, scaling shows 72 reasonable for typical rates.
How important is starting early?
Crucial. Person who saves $5000/year from age 25-65 (40 years) at 7%: ~$1 million. Person who saves $5000/year from age 35-65 (30 years) at 7%: ~$500K. Half. Same total contribution? No — first saved more years. Even better: $5000/year for 10 years (25-35), then nothing, vs $5000/year for 30 years (35-65). First strategy ahead.
How does it apply to debt?
Same principle, opposite direction. Credit card debt at 25% APR: doubles in ~3 years. Compound interest works against you. Reason: pay off high-interest debt aggressively. Mortgage: lower rate, longer term; still significant. $200K mortgage at 5% for 30 years: pay $186K interest. Total >$386K for $200K loan. Compound interest grows debt fast.
What about compounding frequency?
More frequent compounding: more total. Annual: r per year. Monthly: r/12 per month, 12 times per year. Daily: r/365 per day. Continuous: e^(rt). Difference small at low rates; significant at high. Most banks: monthly or daily for savings; depends on contract for loans. Specific to consider.
How does it apply to retirement?
Most important. Long time horizons amplify. Contributing $5000/year for 40 years at 7%: $1 million+. Cost of waiting: huge. Index funds: realistic 7%+ historic returns. 401(k) employer match: doubles your money immediately. Tax-advantaged: huge benefit. Single biggest factor in retirement: starting early and compounding.