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.
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.

Stock Market Tips India

Stock Market Tips,Devang visaria provide a good intarday call as compare other trade, people make profite to use devang visaria tips. 
make money with devang visaria,He is one of the best trader in commodity, equity And Ace market in mumbai.
he deal Share Market Tips, Stock Market Tips, Commodity Tips by through call or mobile sms.
special offer : Paid trials @ Rs. 500 per week

Intraday Calls:charges
Quaterly:     Rs 8,000,                 
Half Yearly:  Rs 14,000,
Yearly:       Rs 23,000

For More Information Visit :