- B = ARⁿ⁻¹ + ARⁿ⁻² ... + AR + A
- = A(Rⁿ⁻¹ + Rⁿ⁻² ... + R + 1),
whence
| Rⁿ⁻¹ | Rⁿ⁻¹ | ||
| (3) B = A | —— | or A | —— |
| R - 1 | r |
The expression in parentheses is a geometric series whose sum may be written in the fractional form shown.
The present worth of B, i.e., of
| Rⁿ⁻¹ | |
| A | —— |
| r |
is found from formula (2) above to be:
| Rⁿ⁻¹ | ||
| A | —— | divided by Rⁿ. |
| r |
Expressed as a formula:
| Rⁿ⁻¹ | |
| (4) P. W. = A | —— |
| Rⁿr |