You're on the right track - it just appears to be some computational errors.
The formula for minimum sample size is:
n = ((Zc * s)/d)^2
where Zc = z score (for 98% confidence, 2-tailed = 2.326)
s = standard deviation = 500
d = margin of error = 10
I got a sample size of n = 13,526 and when multiplied by $5 each, that's $67,630.
Now, force n = 2000, since at $5 per sample, they can only afford $10,000
With n = 2000, figure out what d would be if everything else is held the same, then figure out what Zc would be (and hence the confidence level) if everything else is the same.