Market Problem

[johnjones]

Market Value ($) of an art object t years from now is predicted to be

V(t) = 50,000(10^[(sroot(t))/3].

(a) If you buy this object today for $50,000, and the interest rate remains at 8% p.a. compounded continuously, when should you sell it to maximize present value?
(b) If you sell at this optimal time, what is the net present value of your investment?

I'm not sure what to do. So where exactly do I plug in the 8%? Do I need to take the derivative and set it to zero, to find the local maximum? Also, I don't quite understand 'net present value'? :?: [/i]

 

[johnjones]

Can someone please give me a hint to this? I'm rather lost :'(, thx.

 

[stapel]

...where exactly do I plug in the 8%?

I have no idea. The exercise does not state on what sort of investment the interest is being earned, nor how it relates to the object.

But you're in the class and you've read the book. Might this be referring to something along the lines of holding the object versus selling it and investing the sales price?

Do I need to take the derivative and set it to zero...?

The derivative of what?

I don't quite understand 'net present value'?

This is a technical financial term, and should be defined in your text.

Eliz.

 

[johnjones]

...where exactly do I plug in the 8%?

I have no idea. The exercise does not state on what sort of investment the interest is being earned, nor how it relates to the object.

But you're in the class and you've read the book. Might this be referring to something along the lines of holding the object versus selling it and investing the sales price?

Do I need to take the derivative and set it to zero...?

The derivative of what?

I don't quite understand 'net present value'?

This is a technical financial term, and should be defined in your text.

Eliz.

How would I take the derivative of this:

V(t) = 50,000(10^[(sroot(t))/3].

I got: (50000 * 1/3)(ln 10)(t^0.5)

I think I use the formula A = Pert for continuous compounding.

 

[pka]

Ms. Eliz is correct in that this question seems to be specific to your text.
That said, I can tell you that \(\displaystyle e^{0.08t}\) is the formula for continuous interest at 8%pa.

Using the model \(\displaystyle 10^{\sqrt t /3}\) as the growth rate in the value of the art object, as you can see it will be about 92 years until the value of the art is less than the value of an equal deposit.

It seems to me that this is a judgment, “how much does one value the object?”
But not knowing the exact definition net present value this is all the help we can give.

Here is one suggestion: Look at the difference between the two formulae.

 

[johnjones]

Ms. Eliz is correct in that this question seems to be specific to your text.
That said, I can tell you that \(\displaystyle e^{0.08t}\) is the formula for continuous interest at 8%pa.

Using the model \(\displaystyle 10^{\sqrt t /3}\) as the growth rate in the value of the art object, as you can see it will be about 92 years until the value of the art is less than the value of an equal deposit.

It seems to me that this is a judgment, “how much does one value the object?”
But not knowing the exact definition net present value this is all the help we can give.

Here is one suggestion: Look at the difference between the two formulae.

Thx for the nice graph, pika. Thx for your attempt, Eliz. I think, now at least I understand the question. So it is possible to solve this question without taking the derivative of both functions, eh? In my book, it says Net PV = PV - Cost. :?:

 

[johnjones]

So if the present value is 1577.7379 (y coordinate of the intersection), then I take that and minus the cost. So the cost would be plugging 92 into the original equation?