Compound Interest — The Eighth Wonder of the World

Why This Matters

Albert Einstein reportedly called compound interest the “eighth wonder of the world.” Whether or not he actually said it, the mathematics are undeniable: compound interest is the single most powerful force available to ordinary investors. In Angola, where interest rates on government bonds exceed 20%, compounding works with extraordinary speed — for better or worse.

Simple vs. Compound Interest

Simple interest (juros simples) means you earn interest only on your original investment. If you invest Kz 1,000,000 at 20% simple interest for 5 years, you earn Kz 200,000 each year — always calculated on the original Kz 1,000,000. Total after 5 years: Kz 2,000,000.

Compound interest (juros compostos) means you earn interest on your interest. The same Kz 1,000,000 at 20% compounded annually:

With simple interest: Kz 2,000,000. With compound interest: Kz 2,488,320. The difference — Kz 488,320 — is pure compounding magic. And the effect accelerates over time. After 10 years, compounding yields Kz 6,191,736 versus Kz 3,000,000 with simple interest.

The Three Drivers of Compounding

Compound interest has three levers, and understanding them helps you maximize your wealth:

1. Rate of Return

Higher rates compound faster. Angola’s high-interest environment is actually an advantage here:

• At 10% compounded: Kz 1,000,000 becomes Kz 2,594,000 in 10 years
• At 20% compounded: Kz 1,000,000 becomes Kz 6,192,000 in 10 years
• At 25% compounded: Kz 1,000,000 becomes Kz 9,313,000 in 10 years

A 20% rate does not produce twice the wealth of 10% — it produces nearly 2.4 times as much over 10 years. This is exponential growth.

2. Time

Time is the most important variable. An investor who starts 5 years earlier will dramatically outperform one who invests more money but starts later.

Consider two friends, both earning 20% annually:

• Célia invests Kz 100,000/month starting at age 25, stops at age 35 (10 years, total invested: Kz 12,000,000)
• David invests Kz 100,000/month starting at age 35, continues to age 55 (20 years, total invested: Kz 24,000,000)

At age 55, Célia has approximately Kz 287,000,000. David has approximately Kz 197,000,000. Célia invested half as much money but ended up with 46% more wealth — because her money had more time to compound.

3. Frequency of Compounding

How often interest is calculated and added to your balance matters. Semi-annual compounding (every 6 months) produces more than annual compounding. Monthly produces more than semi-annual.

Kz 1,000,000 at 20% for one year:

• Annual compounding: Kz 1,200,000
• Semi-annual (10% twice): Kz 1,210,000
• Monthly (1.67% twelve times): Kz 1,219,391

Treasury bonds with semi-annual coupons that are reinvested provide semi-annual compounding. Bank deposits that pay monthly interest provide monthly compounding if you reinvest.

Compounding and Reinvestment

The critical insight: compounding only works if you reinvest your returns. A treasury bond paying Kz 200,000 annual coupon only compounds if you use that Kz 200,000 to buy more bonds. If you spend the coupon, you are earning simple interest.

This is why dividend reinvestment plans and coupon reinvestment are so powerful. Every Kwanza of income that goes back into the market starts earning its own returns.

Worked Example: The Power of Starting Now

Amara is 30 years old with Kz 500,000 to invest today, plus she can save Kz 150,000 per month. She plans to invest for 20 years at an assumed rate of 18% (after-tax bond/equity blend).

• Initial investment: Kz 500,000
• Monthly contribution: Kz 150,000
• Annual rate: 18%
• Time: 20 years

Using the compound interest formula with regular contributions:

After 20 years, Amara’s portfolio grows to approximately Kz 313,000,000 — from total contributions of just Kz 36,500,000. Over 88% of her final wealth came from compounding, not from her own savings.

If she waited just 5 years and started at 35 instead, investing the same amounts for 15 years: approximately Kz 108,000,000. Waiting 5 years cost her over Kz 200,000,000 in compound growth.

The Dark Side: Inflation Compounds Too

Just as your investments compound in your favor, inflation compounds against you. At 15.7%, inflation roughly halves your purchasing power every 2.8 years. This is why the lesson on inflation came before this one — you must understand both forces to make rational financial decisions.

The goal is to ensure your investments compound faster than inflation erodes. A net positive real return, compounded over decades, builds genuine wealth.

Key Takeaways

• Compound interest earns returns on your returns — it is exponential, not linear growth
• The three drivers are rate, time, and compounding frequency — time is the most powerful
• In Angola’s high-rate environment (18-22%), compounding works with extraordinary speed
• Reinvestment is essential — spend your coupons and you lose the compounding effect
• Starting early matters more than investing more money later
• Inflation compounds against you at the same time — always think in real terms

Common Mistakes

Spending investment income — Every coupon or dividend you spend instead of reinvesting breaks the compounding chain. Treat investment income as capital, not spending money, especially in your wealth-building years.

Underestimating time’s power — People often think “I’ll start investing seriously when I earn more.” But starting with Kz 50,000/month at age 25 produces more wealth than Kz 200,000/month starting at age 35, given enough time.

Ignoring fees and taxes — A 2% annual fee does not sound like much, but over 20 years it can reduce your final wealth by 30-40%. Minimize costs to maximize the compounding effect.

What’s Next

Compounding requires regular contributions to work its full magic. The next lesson teaches you practical budgeting techniques to find money to invest every month — even on a modest Angolan salary.

Next Lesson: Budgeting for Investment — Finding Money to Grow

Play with the numbers yourself using the Compound Interest Calculator and the Investment Simulator.