Parul

[logistic_guy]

Parul deposited \(\displaystyle \$ 4,000\) in a CD paying \(\displaystyle 6.29\%\) compounded continuously. Find the effective interest rate and use it to find the future value after \(\displaystyle 4\) years. Also, find the future value after \(\displaystyle 4\) years by using the nominal rate.

 

[jonah2.0]

Beer induced hint follows.

Parul deposited \(\displaystyle \$ 4,000\) in a CD paying \(\displaystyle 6.29\%\) compounded continuously. Find the effective interest rate and use it to find the future value after \(\displaystyle 4\) years. Also, find the future value after \(\displaystyle 4\) years by using the nominal rate.

You should arrive at the same future value at the end of 4 years at either rate.

 

[logistic_guy]

Thanks a lot professor Jonah. You are a life saver.



the effective interest rate \(\displaystyle = e^{0.0629} - 1 \approx 0.0649 = 6.49\%\)

 

[jonah2.0]

Beer induced query follows.

Thanks a lot professor Jonah. You are a life saver. ...

How am I a life saver if you've graduated already?

 

[logistic_guy]

If I use \(\displaystyle 6.49\%\), I get:

future value \(\displaystyle = 4000(1 + 0.0649)^4 = 5143.933\)

How am I a life saver?

You are a life saver as I had to read three chapters to answer this question, but instead, I just read your post.

you've graduated already?

Yes, I have in engineering with a GPA of \(\displaystyle 98.25\%\)

Or

\(\displaystyle 3.93 \ \text{of} \ 4\)

 

[jonah2.0]

Beer induced reaction follows.

If I use \(\displaystyle 6.49\%\), I get:

future value \(\displaystyle = 4000(1 + 0.0649)^4 = 5143.933\)

You're better off not rounding and use instead the longer decimal expansion of e^0.0629 - 1 of your calculator. It's a better match for 4000e^(0.0629*4)

...
You are a life saver as I had to read three chapters to answer this question, but instead, I just read your post.

You are presumably referring to the three chapters of the book link(s) that I gave you.
Are you learning mathematics of finance on your own?
Was it not included in your engineering course like accounting 101?
Also, why all the accounting 101 questions if you've already passed accounting 101?

 

[logistic_guy]

You're better off not rounding and use instead the longer decimal expansion of e^0.0629 - 1 of your calculator. It's a better match for 4000e^(0.0629*4)

If I use the nominal rate directly, I get:

future value \(\displaystyle = 4000(1 + e^{0.0629} - 1)^4 \approx 5144.326\)

This is slightly different than the first part.

You are presumably referring to the three chapters of the book link(s) that I gave you.

Yes.

Are you learning mathematics of finance on your own?

No, I am just refreshing. I studied Finance 4 years ago.

Was it not included in your engineering course like accounting 101?

Yes, it was.

Also, why all the accounting 101 questions if you've already passed accounting 101?

Refreshment. Humans tend to forget their yesterday lunch meal. What about four years ago? It is a very long time.

 

[jonah2.0]

Beer drenched ramblings follow.

If I use the nominal rate directly, I get:

future value \(\displaystyle = 4000(1 + e^{0.0629} - 1)^4 \approx 5144.326\)

This is slightly different than the first part.

It is slightly different because you rounded it.
As you can see below, the difference with no rounding is no longer appreciable.

Are you learning mathematics of finance on your own?

No, I am just refreshing. I studied Finance 4 years ago.

You sure have forgotten much about it then.
This type of problem should have been routine for you by now.
You should have been familiar with this particular type of problem from your book, lectures, and notebook. You also seem to be presenting this problem as if it's the first time you've seen it. Did your instructor not prescribe a textbook for this subject?

To paraphrase a Samurai master: It is better to fail in practice and improve on your weak points than to fail in combat.

I don't know why I suddenly mentioned that quote. I'm sure there's a lesson in that samurai quote but I'm just too hammered right now to expand on it; it suddenly projected itself to my mind somehow.

You should have kept a permanent notebook of your solution attempt(s) and confirmation or corrected solution (from your instructor) for each math subject that you took. I have more or less gave a somewhat similar advice to Harpazo 5 years ago; he's not big on appreciating useful advice. You can have a lot of fun looking over your early solution attempts from your notebook especially when you've had 4 or 5 beers already. You just can't help but laugh at some of your silly errors and carelessness from a long time ago in light of your present level of maturity. This is the beer in me talking. I sure hope beer in your culture is allowed.

 

[jonah2.0]

Beer drenched ramblings follow.

Parul deposited \(\displaystyle \$ 4,000\) in a CD paying \(\displaystyle 6.29\%\) compounded continuously. Find the effective interest rate and use it to find the future value after \(\displaystyle 4\) years. Also, find the future value after \(\displaystyle 4\) years by using the nominal rate.

Exercise 3.4.9 from Biehler's book.
Odd numbered with answer key at the back section.