Hi all. I've been wrestling with this problem for a few hours today, along with some others on my course at university. Basically we have to make a model in the modelling & simulation package Stella.

The model is for an annuity where the customer makes an initial one-off payment of £100,000, and then receives a fixed monthly payment until their death. Assuming the life expectancy is 10 years, the APR is either 4%, 6% or 8%, and the interest is compounded monthly, we have to figure out how much the bank should pay out each month.

So, basically we have to figure out how much the payments should be so that, taking into consideration payouts made and compound interest on the remaining capital, after 120 months the capital remaining will be 0.

It all sounds simple enough but it's quite difficult to find an expression that takes into account the decreasing capital due to payments made. i have come up with a couple of expressions so far, and they don't seem to quite work, although they're close.

Trial and error shows that the payouts should be approx. £1012 per month, or thereabouts.

Can anybody help at all? Everybody else I have spoken to has given a trial and error answer, but I am pretty sure that this can be solved analytically. Perhaps it can be solved iteratively?

Thanks to anyone who can offer any advice