formula for compound interest (plus yearly investment)?

Question

I would like the formula for the following:
say i invest $1000 in a fund every year, assume the annual return rate is 10%, how much do i get after 10 years?

I know the formula is : C x ((1+r)^n-1)/(1+r)) x (1-r)
and I would like to know how to come up with this formula??
Is it formula of compound interest + Geometric series??
can anyone elaborate for me? or give me a website to find out the answer??

thanks

I would like to know how to come up with the following formula :
C x ((1+r)^n-1)/r) x (1-r)
where C= capital, r=interest rate, n= no of terms of investment

Answer 1

using the formula for the amount Acorrespondin g to principal P at a rate r%/year for n yearsis given by :
A=P(1+r/100)^n,
I f every year you deposit =P, then thesum of the amounts corresponding to periods invested for 1, 2,3,4,.............10 year are:
P(i+r/100)^1+P*(1+r/100)^2+...........+P(1+r/100)^10.
It is a geometrical progression, with first term, a=P(1+r/100)andcommon ratioR=(1+r/100).
the sumS is given by:
S=a(R^n-1)/(R-1)'
So the reqd. total amount is=P(1+r/100)[(1+r/100)^10-1]/r/100'
=P(100+r)/r{(1+r/100)}^10-1}. with r=10& P=1000

So basically you have to use formula for compound interest and formula for the sum of a GP
How much do I get?I interpreted it as total amount not total compound interest.Unfortunately I did not come up with the formula you cited. But I hope this will help you to solve your problem.

Answer 2

I don't know where you got your formula, but the one I use is:
F = A[((1+r)^n - 1)/r] Where A is the annual amount invested.
If the investment is made at the END of each year.
Derivation:
Start with the basic, F = A(1+r)^(n-1).
Multiply by (1 + r)
(1+r)F = A(1+r)^n +A(1+r)^(n-1) +... A(1+r)^2 + A(1+r)^1
Factoring out A : rF = A[(1+r)^n - 1], and
F = A[((1+r)^n - 1)/r]
For your problem:
F = 1000[((1.10)^10 -1)/0.10] = $15,937.42

Answer 3

For the derivation of the formula see page 42 of
http://www.uwm.edu/Course/IE360-Saxena/three.pdf

The formula that you "know" is not quite so.

The future value of 1000/yr @10% for 10 years is
FV = 1000*15.937 = 15937
Factor from Interest Tables.

Answer 4

If you invest at the beginning of each year and get it at th end of the 10th year the first 1000 will draw interest for 10 years and so on
C =1000(1.10^10+1.10^9 +++1.10)=1000 *(1.1^11-1.1)/0.1=
$17,531.17