When you were born, both of your rich grandparents made a deal with your parents, to do with what money they'll give you for birthdays. Grandad's deal was :

*I'll give you £1 for your first birthday. Then, the amounts that I give you each year will double every time*

and Grandma said :

*I will start by giving you £1 for your first birthday. Then, the amount I give you will be the combined total of all the last birthday presents that I have ever given you up to that point. Plus, every birthday you have that's a multiple of five, I'll give you an extra five pounds.*

a)What amount of money do they each pay you for your 15th birthday

and

Who would have given you the most after 27 years?

a) The amount of money that the grandfather gives can be modeled by the summation series ∑(2^k-1) with index 1 and upper limit 15. The summation is 32,767. The amount of money that the grandmother gives can be represented by the series ∑(2^k-2) with index 2 and upper limit of 17. The summation is 65,554 (my arithmetic may be incorrect).

b) In the end, the grandfather pays the most money. Please correct my if I am wrong on any of this.