Compounding interest formula going awry

[Locoism]

If Po dollars are deposited in an account paying r percent compounded continuously and withdrawals are at a rate of 200t (continuously), what is the amount after T years?

I derived the formula by taking the limit as m -> ∞ of the compounding interest equation P(t) = Po(1+r/m)^mt which gives us P(t) = Po*e^rt. So including the withdrawal rate

- P(t) = Po * e^rt - 200t

And that would be the amount in the account after T years. But my question asks, if r = .1 and Po = $5000, when will the account be empty? My function doesn't cross zero, and I don't understand where I made the mistake.

Can anyone help me?

 

[Mute]

If withdrawals are done at a rate of 200t, then isn't the total amount of money withdrawn between time 0 and t 100t²?

 

[Locoism]

Sorry, the question says withdrawals are at an annual rate of 200t dollars.
I thought about that, tried it out and the question still doesn't work out. I'm really worried about this one...*edit* Actually, I am an idiot. For some reason I got no real roots the first time...
*edit* However the question asks me to consider the case Po = $20 000 and r=0.1. I don't see anything special about this. Intuitively I would say the amount stays constant, but plotting it gives me something completely different...

Thank you for your support :P

 

[Chestermiller]

Sorry, the question says withdrawals are at an annual rate of 200t dollars.
I thought about that, tried it out and the question still doesn't work out. I'm really worried about this one...


*edit* Actually, I am an idiot. For some reason I got no real roots the first time...
*edit* However the question asks me to consider the case Po = $20 000 and r=0.1. I don't see anything special about this. Intuitively I would say the amount stays constant, but plotting it gives me something completely different...

Thank you for your support :P

The rate at which interest is accumulating is Pr, where r is the yearly interest rate divided by 100. The rate at which withdrawals are being made is 200. Therefore, the net rate at which principal is increasing is given by the differential equation:

dP/dt = Pr - 200

 

[blue_raver22]

It seems that you have correctly derived the formula for compounding interest with continuous withdrawals. However, it is important to note that the formula assumes that the withdrawals are made at regular intervals, such as monthly or yearly. In this case, the withdrawal rate of 200t should be divided by the compounding interval, which in this case would be m=∞ (continuous compounding). So the correct formula would be P(t) = Po*e^rt - 200t/m.

Additionally, to find when the account will be empty, you can set P(t) = 0 and solve for t. This will give you the time at which the withdrawals will have depleted the account completely. It is possible that the account may never reach zero, as the compounding interest may continue to offset the withdrawals.

If you are still having trouble with your formula, I suggest double-checking your calculations and making sure all units are consistent. You can also seek assistance from a math or finance expert for further clarification.