General
Compound Interest
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods, causing wealth to grow exponentially over time.
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Exam Tip
Rule of 72: Divide 72 by interest rate = years to double. Compound = exponential growth.
What is Compound Interest?
Compound interest is "interest on interest"—you earn returns not just on your original investment, but also on the gains you've already accumulated. This creates exponential growth over time.
Simple vs. Compound Interest
| Type | Calculation | Growth Pattern |
|---|---|---|
| Simple Interest | Principal × Rate × Time | Linear |
| Compound Interest | Principal × (1 + Rate)^Time | Exponential |
Compound Interest Formula
A = P(1 + r/n)^(nt)
Where:
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate
- n = Times compounded per year
- t = Years
The Power of Compounding
| Investment | Rate | Years | Simple Interest | Compound Interest |
|---|---|---|---|---|
| $10,000 | 7% | 30 | $31,000 | $76,123 |
Compounding Frequency
| Frequency | Times/Year | $10,000 at 10% for 1 year |
|---|---|---|
| Annual | 1 | $11,000.00 |
| Quarterly | 4 | $11,038.13 |
| Monthly | 12 | $11,047.13 |
| Daily | 365 | $11,051.56 |
Rule of 72
Quick way to estimate doubling time: Years to Double = 72 ÷ Interest Rate
At 8% interest: 72 ÷ 8 = 9 years to double