Why post same question twice? It's difficult enough for Guests battling the everlasting Captcha. I must fight up to three or more per post when Captchas are antsy to fight. They must prove themselves to Google to defeat bots. However, I may be defeated as they grow stronger everyday with stealth. I can not spot a car in an ocean yet I fail to see the sky. Here is the answer you seek.
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