Question

initial investment 3000 doubles value 8.3 years. Assuming compound continuously. What is the interest rate? Pe^rt

Answer 1

We can write the following equation from the given information:
\[\large 6000=3000e^{8.3t}\ ............(1)\]
Dividing both sides of (1) by 3000 we get:
\[\large 2=e^{8.3t}\ ............(2)\]
Now we need to solve equation (2) to find the interest rate as a decimal. The first step in doing that is to take natural logs (ln) of both sides of (2). Can you do that?

Answer 2

@sharonholmes1 Are you there?

Answer 3

I here and that's where I got stuck.

Answer 4

The left hand side is simple. For the right hand side you use the following rule of logs:
\[\large \ln e^{x}=x\]
So using that rule what is:
\[\large \ln e^{8.3t}=?\]

Answer 5

@sharonholmes1 Are you there?

Answer 6

I'm here.

Answer 7

Can you answer my last post please.

Answer 8

I got 8.3%

Answer 9

That is not the correct result. Taking natural logs of both sides of (2) we get:
\[\large \ln 2=8.3r\ .........(3)\]
from which the value of r is:
\[\large r=\frac{\ln 2}{8.3}=you\ can\ calculate\]
The value of r must be multiplied by 100 to become a percentage rate.

Note: In my previous postings my equations stated t where it should have been r.

Answer 10

So will it be 8.4% ?

Answer 11

My result to 2 decimal places is 8.35%

Answer 12

That's what I got the first time and you said it was not right. So I thought I had to round it or something...lol.

Answer 13

Your post stated:
"I got 8.3%"
For interest rates taken continuously over a long period, the percentage rate would normally be shown to two decimal places. So if the rate was truly exactly 8.3% it should be shown as 8.30%.

Answer 14

Sorry about that. One of the choices was just 8.3 so I didn't think that the decimal place would have matter.

Answer 15

If the answer was required to one decimal place, then 8.35% would round to 8.4%.

Answer 16

Is 8.4% an answer choice?

Answer 17

Yes. I rounded it to the nearest tenth of a percent.