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What is Compound Interest?
Compound interest is interest calculated on the initial principal and all accumulated interest from previous periods. Unlike simple interest (calculated only on principal), compound interest allows your money to grow exponentially.
Formula: A = P(1 + r/n)^(nt)
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate (as decimal)
- n = Compounding frequency per year
- t = Time in years
How Does Compounding Frequency Affect Returns?
The more frequently interest compounds, the more you earn. However, the difference between frequencies decreases at higher levels.
Example: $10,000 at 5% for 10 years:
- Annual: $16,288.95
- Monthly: $16,470.09 (+$181)
- Daily: $16,486.65 (+$16 more)
What is the Rule of 72?
A quick way to estimate how long it takes for an investment to double:
Years to Double ≈ 72 ÷ Interest Rate
Examples:
- 6% return: 72 ÷ 6 = 12 years
- 8% return: 72 ÷ 8 = 9 years
- 10% return: 72 ÷ 10 = 7.2 years
Why Start Early?
Time is your greatest advantage in investing. Starting early, even with small amounts, can result in more wealth than starting late with larger amounts.
Example:
- Person A: Invests $5,000/year from age 25-35 (10 years, $50,000 total)
- Person B: Invests $5,000/year from age 35-65 (30 years, $150,000 total)
- At 7% annual return, Person A has MORE at age 65 despite investing 1/3 as much!
What About Inflation and Taxes?
Inflation: Reduces purchasing power of your returns. If you earn 7% but inflation is 3%, your real return is about 4%.
Taxes: Reduce effective returns. Interest, dividends, and capital gains may be taxed. Tax-advantaged accounts (IRA, 401k) help preserve compound growth.
Tip: For conservative planning, subtract expected inflation (2-3%) from your return rate.
How to Use Scenario Comparison
The comparison feature lets you evaluate different strategies:
- Compare rates: See how a 1% difference affects long-term wealth
- Compare contribution amounts: Evaluate increasing monthly savings
- Compare time periods: See the benefit of starting earlier
- Compare frequencies: Monthly vs quarterly vs annual contributions
Common Investment Vehicles
- High-Yield Savings: 3-5% APY, very safe, highly liquid
- CDs: 4-6% APY, very safe, locked in for term
- Stock Market: ~10% historical average, higher risk, long-term growth
- Bonds: 3-7% depending on type, moderate risk
- 401(k)/IRA: 7-10% average, tax advantages, retirement focused