# Thread: Saving at the same rate

1. ## Saving at the same rate

Hello, i cant seem to wrap my head around this question

You want to invest 100 dollars every two weeks at 7 percent compounded monthly for the next 40 years. how much money will you have at the end of 40 years?
its driving me to
i would like to see a formula for this that does not involve calculating interst on each instance of 100 dollars for a massive chain equation. you can use 200 invested monthly to make it easier since you only earn interest monthly anyways but man i cant think

2. Originally Posted by ffezz
Hello, i cant seem to wrap my head around this question

You want to invest 100 dollars every two weeks at 7 percent compounded monthly for the next 40 years. how much money will you have at the end of 40 years?
its driving me to
i would like to see a formula for this that does not involve calculating interst on each instance of 100 dollars for a massive chain equation. you can use 200 invested monthly to make it easier since you only earn interest monthly anyways but man i cant think
If you learn basic principles, all the problems look about the same.

We have i = 0.07
n = 40*26 = 1040
i12 = 0.07/12 = 0.00583333.....
i52 = (1+i12)^(6/13) - 1 = 0.0026880919907
r = 1+i52
P = \$100
S = The Desired Accumulation.

That's all we need. Now build it. Note: Accumulations oftern are easier to build from the back.

Considering only the last payment, one week later, we have Pr
The second to last payment is Pr^2

Pr + Pr^2 + Pr^3 + ... + Pr^n = S

Pr(1 + r + r^2 + ... + r^(n-1)) = S

Pr((1 - r^n)/(1 - r)) = S

Ummm...We're about done. You do the rest.

3. Not a single follow up question?!

Where did I get "6/13" and what does that mean?