Compound Interest Formula
Each period's interest is added to the principal before the next period is computed, so interest itself earns interest.
The formula
Bₙ = B₀(1 + R)ⁿ
Interest calculated on both the principal and the accumulated interest from previous periods. Grows exponentially.
What goes into it
- Initial borrowed capital (B₀)
- Number of periods (n)
- Interest rate per period (R, %)
Worked example
Same $100 at 7% — short vs. long horizon:
| Principal (B₀) | $100 |
| Rate / period (R) | 7% |
| Periods (n) | 5 |
| Balance B₅ | ≈ $140.26 |
| Principal (B₀) | $100 |
| Rate / period (R) | 7% |
| Periods (n) | 20 |
| Balance B₂₀ | ≈ $386.97 |
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