Please state the payment periods... I will just assume it's annual.
This is the notation for our problem
PV = A(P/A, i%, n)
Now to set up the formula
PV = A((((1+i)^n)-1)/(i*(1+i)^n)
11000 = 500((((1.005)^n)-1)/(.005*(1.005)^n)
Many methods you could solve for n.
After many guesses I came the value is in between 23 and 24. Furthermore, with linear interpolation I came to the conclusion n=23.4897
Guest #1
Note that there is a direct solution for n in this case:
PV=P{[1 + R]^N - 1 / [1 + R]^N} / R
11,000 = 500 x {[1.005]^N - 1 / [1.005]^N} / 0.005
22 ={1.005^N - 1 / 1.005^N} / 0.005
0.11 = {1.005^N -1 / 1.005^N}, solve for N
[200/201]^N = 89/100 take the log of both sides
N = Log[89/100] / Log[200/201]
N = 23.365
