Year

Allowance if Obsolescence Occurs During the Year

Probability of Obsolescence During the Year

1

$I_0$

$1-{\text{e}}^{-\lambda }$

2

$I_0-I_{0}r$

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

3

$I_0-{\displaystyle \sum _{x=1}^2{I}_{0}r{\left(1-r\right)}^{x-1}}$

${\text{e}}^{-2\lambda }-{\text{e}}^{-3\lambda }$

1 < t < N

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

${\text{e}}^{-\lambda \left(t-1\right)}-{\text{e}}^{-\lambda t}$

N

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

${\text{e}}^{-\lambda \left(N-1\right)}-{\text{e}}^{-\lambda N}$