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Use identical payment and rate assumptions
The fictional stream pays 4 at each period end and discounts at 8% per period. Compare finite payment counts with the infinite-stream model.
Compute each finite present value
| Payment count | PV |
|---|---|
| 5 | 15.9708 |
| 10 | 26.8403 |
| 30 | 45.0311 |
| 100 | 49.9773 |
| Infinite model | 50 |
Explain the remaining difference
Each finite stream omits later payments that have positive present value. Their values become progressively smaller under the positive-rate condition, allowing a finite limit of 4/0.08 = 50.
Keep the convergence condition
This comparison does not extend to a zero or negative rate with the same positive constant payments forever. In those cases the required infinite discounted sum does not converge to C/r.