Geometric Progression

Hi everyone,



I'm not yet preparing for the second exam, but my question seems more relevant here. I hope you don't mind me posting in this section.



Here is my question.



I've got to simulate a capital for a group of people.



For each person, the formula is something like this:



Suppose the person's actual age is 25 years old: (with i being the premium's evolution rate and r being the yield)

25 : premium

26 : premium * (1+r) * (1+i)

27 : premium * (1+r) ^2 * (1+i)^2

etc until the age of 60.



Now I can't keep doing this for each person in the group. I would like a formula to estimate the capital (which is the sum of the terms above) for each person of my group without having to do this series of calculation each time.



It's obvious it's a geometric progression. I'm thinking r is (1+r) * (1+i). However when I do this, my capital is not equal to the sum of the terms I stated above. I can't find where I went wrong.



As an illustration, suppose P = 15 000; i = 4% and r = 4,5%. What do you guy think?



Thanks a lot for your help.



Best,

Geometric Progression