Can anybody explain following Actuarial problems step by step?

Can anybody explain following Actuarial problems step by step?
1.Mohan and John have equal amounts of money to invest. Mohan purchases a 10 year annuity-due with annual payments of Rs. 2500 each. John invests his money in a savings account earning 9% effective annual interest for two years. At the end of two years, he purchases a 15-year immediate annuity with annual payments of Z. If both annuities are valued using an effective annual rate of 8% find the value of Z.
(Answer-Rs.2514.75)
2.In fund X money accumulates at force of interest δt = .01t+.010 for 0

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.

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