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What is Compound Interest?
Albert Einstein reportedly called compound interest “the eighth wonder of the world.” Whether or not he actually said that, compound interest is the single most powerful force in personal finance. It’s the interest you earn on both your original deposit and on the interest that has already been added.
Simple vs Compound Interest
- Simple interest: You earn interest only on the original principal.
- Compound interest: You earn interest on the principal plus all accumulated interest.
Over time, the difference is dramatic:
For $10,000 at 7% over 30 years:
Simple interest: $10,000 + ($10,000 × 0.07 × 30) = $31,000
Compound interest: $10,000 × (1.07)^30 = $76,123
Compound interest earns you $45,123 more.
The Compound Interest Formula
A = P × (1 + r/n)^(n×t)
Where:
A= final amountP= principal (starting amount)r= annual interest rate (decimal)n= number of times interest compounds per yeart= number of years
How Compounding Frequency Matters
For $10,000 at 8% over 10 years:
| Frequency | n | Final Amount |
|---|---|---|
| Annually | 1 | $21,589 |
| Quarterly | 4 | $22,080 |
| Monthly | 12 | $22,196 |
| Daily | 365 | $22,253 |
More frequent compounding earns more, but the difference diminishes.
The Rule of 72
A quick way to estimate how long it takes to double your money:
Years to double ≈ 72 / Interest Rate
| Rate | Years to Double |
|---|---|
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 10% | 7.2 years |
| 12% | 6 years |
The Power of Starting Early
Starting 10 years earlier makes a massive difference. Investing $5,000/year at 7%:
- Start at 25, stop at 65:
$1,068,048 - Start at 35, stop at 65:
$505,365
Starting 10 years earlier with the same contributions nearly doubles your result.
Free Compound Interest Calculator
See how your money grows over time with compound interest.
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Example
$10,000 at 7% compounded monthly for 20 years:
A = 10,000 × (1 + 0.07/12)^(12×20)
A = 10,000 × (1.00583)^240
A ≈ $40,387.39
Total interest = $30,387.39
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal amount. Compound interest is calculated on the principal plus all previously earned interest. Over long periods, compound interest generates significantly more returns because your interest earns interest.
How often should interest compound for the best results?
More frequent compounding produces higher returns. Daily compounding earns more than monthly, which earns more than annually. However, the difference between daily and monthly compounding is small. The bigger factors are your interest rate and time horizon.
What is the Rule of 72?
The Rule of 72 is a quick estimation method. Divide 72 by your annual interest rate to estimate how many years it takes to double your money. For example, at 8% interest, your money doubles in roughly 9 years (72 / 8 = 9).
If you are planning loan payments alongside your investments, try our loan payment calculator to see how interest works on the borrowing side. For business owners tracking revenue, our profit margin calculator can help you understand your earnings.
Model Compound Interest in Notes Calculator
Notes Calculator’s variables and percentage support make it easy to model investment scenarios right in your notepad:
# Investment Growth
principal = 10k
annual rate = 7%
years = 30
// Year-by-year growth
Year 1 = principal + annual rate
Year 5 = principal * (1.07) ^ 5
Year 30 = principal * (1.07) ^ 30
Change principal or annual rate and every line updates instantly. Use total to sum contributions, or add headings with # to separate different investment scenarios in the same tab. Notes Calculator supports large number notation — type 1.2M instead of 1,200,000 for readability.