Compound Interest

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In simple terms, it's "interest on interest," which allows your money to grow exponentially over time.

Albert Einstein allegedly called compound interest "the eighth wonder of the world," saying "He who understands it, earns it; he who doesn't, pays it." This power of compounding is the fundamental principle behind successful long-term investing.

Simple Interest vs. Compound Interest

Simple Interest: Calculated only on the principal

• $1,000 at 5% annual for 3 years = $1,000 + ($1,000 × 0.05 × 3) = $1,150

Compound Interest: Calculated on principal + accumulated interest

• Year 1: $1,000 + ($1,000 × 0.05) = $1,050
• Year 2: $1,050 + ($1,050 × 0.05) = $1,102.50
• Year 3: $1,102.50 + ($1,102.50 × 0.05) = $1,157.63

Difference: $7.63 in just 3 years. Over decades, this difference becomes massive!

Required Data

1. Initial principal - Starting amount to invest
2. Interest rate - Annual percentage rate (APR)
3. Time period - Years to invest
4. Compounding frequency - How often interest is calculated:
   • Annually (1x/year)
   • Semi-annually (2x/year)
   • Quarterly (4x/year)
   • Monthly (12x/year)
   • Daily (365x/year)
5. Additional contributions (optional) - Regular deposits

Compound Interest Formula

A = P(1 + r/n)^(nt)

Where:

• A = Final amount
• P = Initial principal
• r = Annual interest rate (decimal)
• n = Compounding frequency per year
• t = Time in years

With Regular Contributions

A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) - 1) / (r/n)]

Where PMT = periodic payment amount

Situation: You're 30 years old and want to retire at 65 with a substantial nest egg. You have $5,000 saved and can contribute $300 monthly. Your investment returns 7% annually (historical stock market average). How much will you have at 65?

Data:

• Initial principal (P): $5,000
• Monthly contribution (PMT): $300
• Annual rate (r): 7% = 0.07
• Compounding frequency (n): 12 (monthly)
• Time (t): 35 years (65 - 30)

Step-by-step calculation:

1. Grow initial $5,000:

   • A₁ = 5,000(1 + 0.07/12)^(12×35)
   • A₁ = 5,000(1.00583)^420
   • A₁ = 5,000 × 10.677
   • A₁ = $53,385

2. Grow monthly contributions:

   • A₂ = 300 × [((1.00583)^420 - 1) / 0.00583]
   • A₂ = 300 × [(10.677 - 1) / 0.00583]
   • A₂ = 300 × 1,659.11
   • A₂ = $497,733

3. Total at age 65:

   • Total = $53,385 + $497,733
   • Total = $551,118

Results:

• You contributed: $5,000 + ($300 × 12 × 35) = $131,000
• You earned in interest: $551,118 - $131,000 = $420,118
• Interest is 3.2 times your contributions!

Key insight: Starting early is crucial. If you waited until age 40 to start (10 years later), you'd have only ~$245,000, less than half!

Starting at different ages (same conditions):

Lesson: Those 5 extra years from 25-30 add over $200,000! Time is your greatest asset.

✅ Start as early as possible: Even small amounts compound significantly over decades. $50/month from age 20 beats $200/month from age 40.

✅ Be consistent: Regular contributions matter more than timing the market. Dollar-cost averaging smooths out volatility.

✅ Reinvest dividends: Choose funds that automatically reinvest dividends to maximize compounding.

✅ Higher frequency is slightly better: Monthly compounding yields slightly more than annual, but the difference is small compared to rate and time.

✅ Don't withdraw early: Breaking compound growth early costs enormous long-term gains. That $10,000 withdrawal at age 30 costs you $107,000 at age 65!

✅ Increase contributions with raises: When you get a raise, increase your contribution by 50% of the raise amount. You won't miss it, but future you will thank you.

What's a realistic interest rate for calculations?

• Conservative (bonds/savings): 3-4%
• Moderate (balanced portfolio): 5-6%
• Aggressive (stocks): 7-10%
• Historical S&P 500 average: ~10% (but with volatility) Use 6-7% for realistic long-term planning.

How does inflation affect compound interest?

Inflation reduces purchasing power. If you earn 7% but inflation is 3%, your "real return" is only 4%. Always consider real (inflation-adjusted) returns for long-term planning.

Should I pay off debt or invest?

Compare interest rates. If credit card charges 18% and investments earn 7%, pay off debt first. If mortgage is 3.5% and you can earn 7% investing, you might invest while paying minimum on mortgage.

What's the Rule of 72?

Divide 72 by your interest rate to estimate how many years it takes to double your money. At 8%, 72÷8 = 9 years to double. Quick mental math for compounding!

Can compound interest work against me?

Yes! Credit card debt compounds against you. A $5,000 balance at 20% APR becomes $6,000 in one year, $7,200 in two years if you don't pay it down. Always pay off high-interest debt first.

Do I need a lot of money to start?

No! Even $25/month matters. Starting with $25/month at age 20 at 7% gives you $60,000 by age 65. Don't wait for "enough money" – start now with what you have.