Compound interest: the eighth wonder of the world
Albert Einstein is often credited with the phrase: "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who does not, pays it." Although the attribution is debated, the concept is undeniable.
Compound interest is the reason investing early is so powerful. You not only earn interest on your initial capital, but also on the interest already accumulated, creating a snowball effect that accelerates the growth of your money.
Compound interest formula
Where:
- A = Final amount (principal + interest)
- P = Initial principal (main investment)
- r = Annual interest rate (as a decimal, e.g. 10% = 0.10)
- n = Number of times it compounds per year
- t = Time in years
When regular monthly contributions are included, the formula incorporates an additional geometric series that this calculator solves automatically.
A practical example of compound interest
Let's see how an investment of $5,000,000 with monthly contributions of $200,000 grows at 10% per year:
- After 5 years: ~$23,500,000 (you contributed $17,000,000)
- After 10 years: ~$49,000,000 (you contributed $29,000,000)
- After 20 years: ~$148,000,000 (you contributed $53,000,000)
- After 30 years: ~$420,000,000 (you contributed $77,000,000)
Notice how the interest far exceeds your contributions as time goes by. That is the power of compound interest.
Compound interest vs. simple interest
The key difference is that simple interest is only calculated on the original principal, while compound interest is calculated on the principal plus the accumulated interest.
With $10,000,000 at 10% per year over 20 years:
- Simple interest: $10,000,000 + ($10,000,000 × 10% × 20) = $30,000,000
- Compound interest: $10,000,000 × (1.10)^20 = $67,275,000
Compound interest generates more than double over the same period.
The Rule of 72
A quick way to estimate how long you need to double your money:
- At 6% per year: 72/6 = 12 years
- At 8% per year: 72/8 = 9 years
- At 10% per year: 72/10 = 7.2 years
- At 12% per year: 72/12 = 6 years
Where to invest for compound interest in Latin America
- Fixed-term deposits: The most conservative option. Rates of 5-15% depending on the country.
- Investment funds: Professional diversification with potentially higher returns.
- Stock market: Stocks and ETFs with dividend reinvestment.
- Digital platforms: Nu, Mercado Pago and other fintechs offer daily returns on your balance.
- Government bonds: Fixed income backed by the state.
Frequently asked questions about compound interest
Compound interest is interest calculated on the initial principal plus the accumulated interest from previous periods. Unlike simple interest, which is only calculated on the original principal, compound interest lets your money grow exponentially over time.
The basic formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the compounding frequency per year, and t is the time in years.
The higher the compounding frequency, the more you earn. Monthly compounding generates more than annual compounding. However, the difference between daily and monthly compounding is minimal. The most important factors are the interest rate and time.
Use the Rule of 72: divide 72 by your annual interest rate. For example, at 8% per year, your money doubles in 72/8 = 9 years. At 12%, it doubles in 6 years.
Options include: fixed-term deposits with automatic renewal, investment funds, stocks that reinvest dividends, savings accounts with interest compounding, and digital investment platforms such as Nu, Mercado Pago, among others.