What is the criteria for any company to be listed in BSE or NSE?

Also can the same company be listed in both the stock exchanges? Also how the points goes up or down in a day? Suppose if a company goes for M&A,does it mean the Value of shares or the points in the SENSEX of the company necessarily goes up? or the reverse. Suggest me any book or website to understand the basic things of teh stock market…

A calculus problem on continuous annuity with withdrawal.?

Show that a continuous annuity with withdrawal rate N = $5000/yr and interest rate r = 8%, funded by an initial deposit of Po= $75,000, never runs out of money.

As I understand the differential equation for this type of problem is
dP/dt = r (P-N/r)
For r, I should substitute 8/100 = 0.08. Is this correct?
This is how I solved the equation:
dP/(P – N/r) = r dt
ln(P – N/r) = rt + ln(C), where C is a constant
ln(P – N/r) – ln(C) = rt
ln[(P – N/r)/C] = rt
P – N/r = C e^rt
P = N/r + C e^rt
Substituting the given value of P at t = 0, we can find the value of C. I got C = $12500
P = N/r + 12500 e^rt
P = 5000/.08 + 12500 e^rt
P = 62500 + 12500 e^(.08t)
From the above equation, P > 0 for all values of t. Therefore the annuity never runs out of money.
Is my analysis correct?
What surprises me is the equation P = N/r + C e^rt
Since N is the withdrawal rate, should we not get an equation which shows that P decreases when N increases? But the equation P = N/r + C e^rt shows just the opposite.