Since the conversion must be sincere and there is absolute tranparency where god or whatever judge has omniscience to know if the conversion is sincere.
You're not appreciating the nature of the dynamic decision-making, with backwards induction used to construct optimal behaviour over the individual's lifetime. Let us first give an example that assumes certainty. You know you're going to die when you reach 80. The rational forward-thinker will appreciate that once he makes 79 he will switch and invest into the after-life. He knows that there isnt an investment rule: he doesn't have to invest a given level of years in church/Jesus. He just needs to ensure sincerity and, given death is fast approaching, he knows that the 79 year old version of him will achieve that requirement and after-life utility is gained. Given he knows how the 79 year old will behave, it becomes rational for the younger version to avoid the costs associated with religion (until he reaches 79).
There are only two questions with this approach. First, we have to assume that religion is costly. We therefore have to adopt the neoclassical approach to household production (see the stuff by Gary Becker). Religion is costly because of the time investments required, which ensure opportunity costs have to be considered (These costs then increase substantially as fundamentalism increases). Second, we have assumed certainty. Clearly, thats a naive assumption to make. Once we introduce uncertainty we then have to factor in risk aversity. One could, for example, assume that a linear path where the attractiveness of church investment increases with age. However, that certainly would suggest sincerity is going to be a problem. Its much more likely to lead to the discrete choice switch from non-believer to believer at an earlier age (suggesting that young church goers are, ceteris paribus, more risk averse).
But lets explore the rationality of religion by itself.
The debate is over the nature of bounded rationality. We have two available models, depending on your stance, where we can indicate the constraints on the individual's maximisation behaviour:
(1) The myopic party fiend
This person may endeavour to construct optimal plans, where behaviour is effectively curtailed to ensure the maximisation of after-life utility. However, he/she is undone by the urge to maximise today's fun factor and therefore consumes 'sin products'.
(2) The madhatted god-botherer
This person restricts his/her behaviour such that utility maximisation cannot be achieved. Religion has to be understood as an external influence limiting free will, rather than as an investment in social capital. Alternatively, one can borrow from sociology analysis and argue that religion is an offshoot of our primitive past (limiting rational maximisation behaviour)
Of course, if you want to present a report
Why would I present a report? I'm far from convinced in the applicability of using neoclassical theory on these topics. I'm more interested in the methods to critically analyse the approach, rather than to offer some notion of economic truth.
I can offer reading to aid your understanding of how its used. The main writer in the field is Laurence R. Iannaccone. I look forward to any relevant critique of the nature of his work. I'm interested in the relevance of the approach and the limits of neoclassical theory in explaining social behaviour