Year

Allowance if No Obsolescence Risk

Probability of No Obsolescence in Given Year or Previous Years

1

$I_{0}r$

${\text{e}}^{-\lambda }$

2

$I_{0}r\left(1-r\right)$

${\text{e}}^{-2\lambda }$

3

$I_{0}r{\left(1-r\right)}^2$

${\text{e}}^{-3\lambda }$

1 < t < N

$I_{0}r{\left(1-r\right)}^{t-1}$

${\text{e}}^{-\lambda t}$

N

$I_0-{\displaystyle \sum _{x=1}^{N-1}{I}_{0}r{\left(1-r\right)}^{x-1}}$

${\text{e}}^{-\lambda N}$