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?(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Compounding interest formula going awry

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