CalculateY
How Compound Interest Really Works
Compound interest is often called the most powerful force in finance. But what does it actually mean, and why does it matter so much for long-term investing?
Simple Interest vs. Compound Interest
With simple interest, you earn interest only on your original deposit. If you invest $10,000 at 5% simple interest, you earn $500 per year, every year. After 10 years, you have $15,000.
With compound interest, you earn interest on your interest. That same $10,000 at 5% compounded annually becomes $16,288.95 after 10 years. The extra $1,288.95 comes entirely from earning interest on previously earned interest.
The Compound Interest Formula
The standard formula is:
A = P(1 + r/n)^(nt)
Where:
- A = the estimated future value
- P = the principal (your initial investment)
- r = the annual interest rate (as a decimal)
- n = the number of times interest compounds per year
- t = the number of years
How Compounding Frequency Matters
The more frequently interest compounds, the more you earn. Here is what $10,000 at 5% looks like over 10 years with different compounding frequencies:
- Annually: $16,288.95
- Quarterly: $16,436.19
- Monthly: $16,470.09
- Daily: $16,486.65
The difference between annual and daily compounding on a $10,000 investment is about $198 over 10 years. The effect is real but modest. Where compounding frequency matters more is at higher rates or over longer periods.
Why Starting Early Matters
The real power of compound interest is time. Consider two investors:
Investor A starts at age 25 and invests $200/month for 10 years, then stops contributing entirely. Total invested: $24,000.
Investor B starts at age 35 and invests $200/month for 30 years, never stopping. Total invested: $72,000.
At a 7% average annual return, by age 65:
- Investor A has approximately $353,000
- Investor B has approximately $227,000
Investor A invested less than a third as much money but ended up with more, because those early contributions had 30 extra years to compound. This illustrates the importance of starting early, even with small amounts.
The Rule of 72
A quick way to estimate how long it takes your money to double: divide 72 by the annual interest rate.
- At 6%: approximately 12 years to double
- At 8%: approximately 9 years to double
- At 10%: approximately 7.2 years to double
This is an approximation, but it is surprisingly accurate for rates between 2% and 15%.
Key Takeaways
Compound interest rewards patience and consistency. The three factors that matter most are:
- Time: the longer your money compounds, the more dramatic the growth
- Rate: even small differences in rate compound into large differences over decades
- Contributions: regular additions amplify the compounding effect
The best time to start investing was yesterday. The second best time is today.