
Cash value
Hi
I have the following problem:
The number of customers in the first year is 4000. Each year the number of cuatomers increases by 1000 (t1=4000,t2=5000...tn=3000*1000n). Farther, each customer is to pay an annual fee F. r is thd interest rate. I got to find the cash value of the aernings of this company in year t.
The cash value of the earnings in year t is (3000+1000t)F/r^t.
The whole cash value until year t is the cash value of every year until year t added, thus
4000F/r+5000F/r^2+6000F/r^3(...)+(3000+1000t)F/r^t.
This equals F(4000r^(t1)+5000r^(t2)...+3000+1000t)/r^t
If you leave by side F/r^t, i need to find the sum of 4000r^(t1)+5000r^(t2)...(3000+1000t)r^0. however i dont get how to do it, as rhis is a mixture of the arithmetric series 3000+1000t and the geometric series r^t.
Anyone knows how to do that?
Thanks
Schdero

Re: Cash value
try and write down the problem in summation notation. You'll find its the sum of a geometric series and a hypergeometric series. Hoppefully you were taught how to sum those before being given the problem.
If that language is unfamiliar, Alternatively you might say it can be expressed as the sum of a level annuity and an increasing annuity.