Thread: L' Hospital's Rule

if an initial amount A₀ of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is

A = A₀ (1 + r/n )^nt

if we let n->infinity we refer to the continuous compounding of interest, use L' Hospital's Rule to show that if interest is compounded continuously, then the amount after t years is

A = A₀ e<sup>rt

.....i dont understand how to get from the first amount to the second using l' hospital's rule</sup>

what are the constants in this? please help!!!!

You are being asked to compute:



where are constants.





To use L'Hôpital's rule, so you need to get it into the indeterminate form or .

Try taking the natural log of both sides, and use the properties of limits and logs to get one of these forms.

is t a constant also?

Originally Posted by MarkFL2

You are being asked to compute:



where are constants.





To use L'Hôpital's rule, so you need to get it into the indeterminate form or .

Try taking the natural log of both sides, and use the properties of limits and logs to get one of these forms.

Yes, I just edited my post to include t. Sorry about that.

The way I worked it, I had to apply L'Hôpital's rule twice.

thank you for all your help! you are so nice!!!

Glad to help, and if you get stuck, post your work, and I will be glad to offer further guidance.

i think i got this one but do you think you could look at my other posts and give me some advice please?

Originally Posted by MarkFL2

Glad to help, and if you get stuck, post your work, and I will be glad to offer further guidance.

I just got a call to leave, but when I get back, I will.

Thank you so much!

Originally Posted by pnfuller

if an initial amount A₀ of money is invested at an interest rate r compounded n times a year, the value of the investment after t years is A = A₀ (1 + r/n )^nt

If you are doing many of these the learn that