1. ## Compound interest problem

You are investing money at 5.7 percent annual interest, compounded continuously. It will take you how many years to double your investment?

2. Originally Posted by thebristolsound
You are investing money at 5.7 percent annual interest, compounded continuously. It will take you how many years to double your investment?
The formula for compount interest is

$\displaystyle A = P(1 + r)^n$.

Here, $\displaystyle r = 5.7\%, A = 2P$

So $\displaystyle 2P = P\left(1 + 5.7\%\right)^n$

$\displaystyle 2 = \left(1 + \frac{5.7}{100}\right)^n$

$\displaystyle 2 = \left(\frac{1057}{1000}\right)^n$

$\displaystyle \ln{2} = \ln{\left[\left(\frac{1057}{1000}\right)^n\right]}$

$\displaystyle \ln{2} = n\ln{\left(\frac{1057}{1000}\right)}$

$\displaystyle n = \frac{\ln{2}}{\ln{\left(\frac{1057}{1000}\right)}}$

$\displaystyle n = \frac{\ln{2}}{\ln{1057} - \ln{1000}}$.

3. I got the answer 12.5038 and it wasn't quite correct, did I miss a step somewhere?

4. It asks you for a whole number of years.

So if it's a little more than 12...

5. It actually asks me to be within one tenth of one percent so 3 numbers beyond the decimal point. I'm sorry for not specifying that. Did I just miss something in my calculations?

6. Can't you round this to 3 decimal places?

$\displaystyle 12.5038 \approx 12.504$.

7. Yeah, it's an online homework problem and the system isn't accepting it, for some reason

WeBWorK : math1050fall2009-1 : 9 : 1

I don't know if you can access that, but thank you so much for the help

8. What does it mean by "compounded continuously?"

How often does it get compounded... I assumed that it was every year, since the interest rate is given per year, but the wording makes me think otherwise...

9. I'm going to try and use the formula A = Pe^rt I think this is what it's looking for

10. Continuous interest is calculated using $\displaystyle Pe^{rt}$

@Prove It
Continuous interest is basically compounded interest that is compounded over such small periods of time, that it is continuous.

11. Yes, I just did some research on that.

It seems that when the number of times the interest is compounded $\displaystyle \to \infty$, the interest tends to

$\displaystyle \lim_{t \to \infty}P(1 + r)^t$

$\displaystyle = Pe^{rt}$.

12. Thanks guys, after finding out that formula I was able to solve it like this

if money is invested at percent and compounded continuously, then the factor multiplying the initial investment after years is given by
To find the time at which the initial investment is doubled we solve the equation
Taking the natural logarithm on both sides and dividing by yields
which with our value of percent gives a value of

13. Still didn't invested but in plane to invest.....

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Compound Interest Formula