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
See the pattern already?
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.