Complete Guide to Compound Interest
What is compound interest?
Compound interest is the process by which the interest earned on an investment is added to the principal, so that new interest is calculated on the total accumulated amount. This creates an "interest on interest" effect that makes money grow exponentially over time.
Unlike simple interest, where you only earn interest on the original principal, compound interest allows you to earn interest on your previous interest. This difference may seem small at first, but over time it becomes a significant advantage for your savings and investments.
The compound interest formula
A = P × (1 + r/n)^(n×t)
Where:
- A = Final accumulated amount
- P = Principal (initial investment)
- r = Annual interest rate (as decimal)
- n = Number of times interest compounds per year
- t = Time in years
Practical example
If you invest $10,000 at an 8% annual rate compounded monthly for 20 years, you'll end up with approximately $49,268. That means you'll have earned $39,268 in interest alone—nearly 4 times your initial investment.
The compounding frequency matters: the more frequent (monthly vs annual), the higher the final return, although the difference is usually marginal.
Frequently asked questions
Simple interest is calculated only on the initial principal, while compound interest is calculated on the principal plus accumulated interest. For example, with $1,000 at 5% annual, simple interest always generates $50/year. With compound interest, the second year earns interest on $1,050, not $1,000.
Compounding can be annual, semi-annual, quarterly, monthly, or even daily. The more frequent the compounding, the higher the total return. However, the difference between monthly and daily compounding is usually minimal.
Regular contributions significantly amplify the power of compound interest. Even small monthly contributions can generate large sums over the long term thanks to the multiplying effect of time and compounding.
The Rule of 72 is a shortcut to estimate how many years it takes for an investment to double. Simply divide 72 by the interest rate. For example, at 8% annual, your money doubles approximately every 9 years (72 ÷ 8 = 9).
For investments and savings, yes. But remember that debts can also accumulate compound interest, making them grow quickly if not paid off. That's why it's important to pay off high-interest debt as soon as possible.
Comparison: Simple vs compound interest
To better understand the power of compound interest, let's see how a $10,000 investment at 8% annual grows over different periods:
| Years | Simple Interest | Compound Interest | Difference | |-------|-----------------|-------------------|------------| | 5 | $14,000 | $14,693 | +$693 | | 10 | $18,000 | $21,589 | +$3,589 | | 20 | $26,000 | $46,610 | +$20,610 | | 30 | $34,000 | $100,627 | +$66,627 |
As you can see, the difference becomes exponential over time. This demonstrates why Einstein reportedly called compound interest "the eighth wonder of the world".
Related calculators
Complement your financial planning with these tools:
- Percentage Calculator - Calculate discounts, increases, and percentage changes
- Rule of Three Calculator - Solve proportions for quick estimates