# Thread: Urgent! Need help with Differential Compound Interest Rate Problem!

1. ## Urgent! Need help with Differential Compound Interest Rate Problem!

Find the amount in a savings account after one year if the initial balance in the account was \$1000, the interest is paid continuously into the account at a nominal rate of 10% per annum(compounded continuously), and the account is being continuously depleted(by taxes say) at the rate of y^2 per million dollars per year. The balance in the account after t years is given by y=y(t). How large can the account grow? How long will it take the account to grow to half of this maximum balance?

I've worked out that dy/dt=0.1y-y^2/10^6
y=y^2/20-y^3/(3*10^6)

I dont know what to do from here since I'm not really sure how to deal with the ys in the function equation above.
ANY HELP will be greatly appreciated!!!!!!!!!!
$\displaystyle \frac{dy}{dt} = 0.1y-10^{-6}y^2 \implies \frac{dy}{ 0.1y-10^{-6}y^2} = dt$