financial maths & calculus

[Goofy]

Please check if my answers are correct, I'm not sure how to conclude d) and how to do e).

 

[Deleted member 4993]

Please check if my answers are correct, I'm not sure how to conclude d) and how to do e).

I think you have interpreted the given equation incorrectly. I think it is:

\(\displaystyle \frac{dS}{dt} \ = \ \ 2000\left(\frac{r}{100}\right)e^{(100^{-1})rt}\)

\(\displaystyle \frac{dS}{dt} \ = \ \ 2000\left(\frac{r}{100}\right)e^{(\frac{rt}{100})}\)

Now integrate......

 

[Goofy]

I think you have interpreted the given equation incorrectly. I think it is:

\(\displaystyle \frac{dS}{dt} \ = \ \ 2000\left(\frac{r}{100}\right)e^{(100^{-1})rt}\)

\(\displaystyle \frac{dS}{dt} \ = \ \ 2000\left(\frac{r}{100}\right)e^{(\frac{rt}{100})}\)

Now integrate......

 

[Steven G]

Please check if my answers are correct, I'm not sure how to conclude d) and how to do e).

You made two major mistakes. First [math]\dfrac{dS}{dt}\neq \int \dfrac{dS}{dt}dt \hspace{.25cm}since \int \dfrac{dS}{dt}dt = S(t)[/math]. You really need to know this!

2nd mistake is that after you found S(t) you found S'(t) = 99r^{99rt} [math]\neq\dfrac{dS}{dt}[/math]. You do know that S'(t) = [math]\dfrac{dS}{dt}[/math]? You were asked to verify your result, not just accept it!

 

[Goofy]

You made two major mistakes. First [math]\dfrac{dS}{dt}\neq \int \dfrac{dS}{dt}dt \hspace{.25cm}since \int \dfrac{dS}{dt}dt = S(t)[/math]. You really need to know this!

2nd mistake is that after you found S(t) you found S'(t) = 99r^{99rt} [math]\neq\dfrac{dS}{dt}[/math]. You do know that S'(t) = [math]\dfrac{dS}{dt}[/math]? You were asked to verify your result, not just accept it!

Thank you, but how do I verify then ? because I thought since the mark allocation is 1, all I needed to do was make sure that my derivative still came out of the integral.

 

[Deleted member 4993]

Thank you, but how do I verify then ? because I thought since the mark allocation is 1, all I needed to do was make sure that my derivative still came out of the integral.

You have calculated:

S(t) = 2000 * \(\displaystyle e^{(\frac{r * t}{100})}\)

to verify it (that it will give back the same expression as given in your question) - you would have to differentiate it:

\(\displaystyle \frac{dS(t)}{dt} = 2000 * \frac{d}{dt}\left[ e^{(\frac{r * t}{100})}\right] \)

\(\displaystyle S'(t) \ = \frac{dS(t)}{dt} = 2000 * \left( \frac{r}{100}\right) * \left[ e^{(\frac{r * t}{100})}\right] \) ...................... same as original given equation

 

[Goofy]

Oh I get it, thank you. Are the rest of the answers correct ? I'm still not sure how to conclude d) and how to approach e).

 

[Deleted member 4993]

Oh I get it, thank you. Are the rest of the answers correct ? I'm still not sure how to conclude d) and how to approach e).

Hint for (e):

\(\displaystyle S(t) \ = \ 2000 * e^{(\frac{r∗t}{100})}\)

S(t) = 2500

2500 = \(\displaystyle 2000 * e^{(\frac{r∗t}{100})}\)

Solve for 't' using "log".

 

[Goofy]

Hint for (e):

\(\displaystyle S(t) \ = \ 2000 * e^{(\frac{r∗t}{100})}\)

S(t) = 2500

2500 = \(\displaystyle 2000 * e^{(\frac{r∗t}{100})}\)

Solve for 't' using "log".

 

[Steven G]

Thank you, but how do I verify then ? because I thought since the mark allocation is 1, all I needed to do was make sure that my derivative still came out of the integral.

Are you serious? You were given dS/dt. Then you found S(t). Then you were asked to use the S(t) you found to compute S'(t). All they asked you were to verify that the S'(t) that you found was what they told you dS/dt equaled. This was just a visual check and when you saw that your S'(t) did not match what you were given then you knew that you made a mistake. Even if they did not advise you to verify your S'(t) you should have done it on your own.

 

[Goofy]

Are you serious? You were given dS/dt. Then you found S(t). Then you were asked to use the S(t) you found to compute S'(t). All they asked you were to verify that the S'(t) that you found was what they told you dS/dt equaled. This was just a visual check and when you saw that your S'(t) did not match what you were given then you knew that you made a mistake. Even if they did not advise you to verify your S'(t) you should have done it on your own.

Okay look, I came here to ask for assistance, not for you to make me feel stupid. If you're gonna have an attitude then please don't bother to assist, but thanks for your help.