What is the difference between the sum of a Geometric Series, whose 1st. term is 1, common ratio 10% and the number of terms 100, and exactly this same Geometric Series, whose terms from 1 to 100 earned interest at 5% compounded annually for 100 years! Thanks for help
1) Using the well-known formula for the sum of geometric series: Sum=F x (1 - R^n) / (1 - R), we get:
=137,796.12
2) For each term to get interest at 5%, will have to sum them up on any good calculator, such as Wolfram/Alpha as follows: ∑(1.10^n)(1.05)^(99-n), from n=0 to 99
=$272,982.22. Here is the link: http://www.wolframalpha.com/input/?i=%E2%88%91(1.10%5En)(1.05)%5E(99-n),+from+n%3D0+to+99
3) The difference between 2 and 1 above is:$272,982.22 - $137,796.12 =$135,186.10 interest only.
