The gamma process is a stochastic cumulative process that can be used to model a time-variant uncertain process. Professor van Noortwijk's research work played a key role in modeling degradation by gamma process and making it popular in engineering community. The maintenance optimization models mostly use the renewal theorem to evaluate the asymptotic expected cost rate and optimize the maintenance policy. However, many engineering projects have relative short and finite time horizon in which the application of the asymptotic formula becomes questionable. This paper presents a finite time model for computing the expected maintenance cost and investigates the suitability of the asymptotic cost rate formula.