Piggy Bank would like to examine the required sample size needed to be
able to estimate the mean dollars that each card holder will spend
each month. It would like to be within plus or minus $10 of the true
mean with a 98% confidence level. The standard deviation is thought to
be $500. How many card holders should be sampled? After you?ve
determined how many card holders should be sampled, PiggyBank comes
back and says that it will cost $5 per sample and they were only
planning on spending $10,000 on the sample. In a memo to the PiggyBank
product development team indicate how many card holders should be
sampled to meet the original requirements of the sample. Then explain
the trade-offs that will occur when you lower the sample to $10,000 to
meet their budget.

In real life, the answer probably has little to do with statistics,
but a lot to do with marketing.
The consulting firm has to judge how much Piggy Bank can be talked
into exceeding the budgeted $10,000 and present a memo that seems to
show that for that greater amount it will be able to provide
statistics of the desired confidence level.
The firm could be cagy, and admit that even for that amount, the
confidence level would still be too low, that for 98% CL, the bank
needs to spend considerably more.
Either the bank goes for 98%, or it accepts the over-budget number of
samples, accepting that it is getting a less accurate result  (which
lets the consulting firm off the hook if its statistics don't seem to
be in line with the bank's experience).

I know, that isn't the answer that you need.

An old cynic.