Calculating Depreciation

[mickgreen58]

The original value of machine X is V dollars, while the original value of machine Y is 2V dollars. Both machines depreciate in value at a constant rate of 10 percent of their original value per year.

 

How to find:

The value of machine X after 3 years

The value of machine Y after 6 years

[mickgreen58]

What I tried to do is:

Let V = 100

 

X = 100

Y = 200

 

But finding the value of X and Y after a couple of years gets nasty:

 

So would you all just do the calculation or is there a faster way?

[Dynamo]

Imo

V(1-10/100)^3

2v(1-10/100)^6

[krovvidy]

IMO it's :-

 

v (1-3*10/100)

&

2v (1-6*10/100)

 

because, it's been given in the qn stem that "Both machines depreciate in value at a constant rate of 10 percent of their original value per year."

[mickgreen58]

Thanks for the feedback, I will study this.

 

The only answer is that Machine Y after 6 years > Machine X after 3 years

[Dynamo]

Once again Krovvidy you are right and I am duh! :)

[mickgreen58]

Kroviddy, let me ask you a question.

 

For equation 1:

 

V = 100

Using a calculator = 72.9

Using your equation: = 70

 

So does your equation serve to get me to a very close value or is it suppose to be exact?

 

I am sure you are right, I am just trying to understand for myself.

[krovvidy]

No approximation ... I think, you should get 70 ... it's an exact value ...

 

I derived it like this:

 

v - v*10/100 ---> after 1st year

v - v*10/100 - v*10/100 ---> after 2nd year

v - v*10/100 - v*10/100 - v*10/100 ---> after 3rd year

i.e., v(1-3*10/100) ...

 

HTH

[skawal]

i dont know the actual formula for the depreciation value.but i think mick, go on with your way.plugging numbers could be one of the best way for the problem.72.9 was mine ans too.

 

krov and dynamo, is this a formula for depreciation?

[krovvidy]

@skawal, If you understand the concept here, probably you don't need to memorize a formula ...

 

It's understood that every year some percent of the initial amount would be lost in depreciation ... we need to see how much would be the depreciated amount after 3 or 6 years ... in my second explanation above you can see the way it's derived ...

 

If let's say the qn stem was as follows:

The original value of machine X is V dollars, while the original value of machine Y is 2V dollars. Both machines depreciate in value at a rate of 10 percent of per year.

 

In such case, it would be the compound interest formula (with a -ve interest rate) ... then Dynamo's solution would've been correct ...

 

HTH ...

[tytyros]

straightline deperciation

P*(1 – NR/100)

compound depreciaiton

P*(1 – R/100)^n