A certain piece of equipment is available from two different manufactu

Question

A certain piece of equipment is available from two different manufacturers. Either can be purchased for $40,000. The machine from Company A depreciates $2,500 per year and has a life span of 15 years. The machine from Company B loses 10% of its value each year and has a 20-year life span. Find the scrap value of each machine to the nearest dollar.

tabishkazi · Accepted Answer

how to calculate 0.9^20 fast? if somebody can help me with it.

pudu · Answer

B is losing 10% per year ..i.e 4000 and life is 20... so depreciation per year is 2000. then how does it has scrap value? please help me to understand it

Ash381 · Answer

For Machine A, Value reduces by 2500 each year. so by 15 years, value would have reduced by 2500*15=37500. Therefore, Scrap value = 40000-37500 =  2500 
For Machine B, values reduces by 10% each year. so by 20 years, scrap value will be 40000*(0.9)^20 =  4863 . 0.9 signifies the value after losing 10% value.

Ash381 · Answer

Since 10% value is lost every year, depreciation for year 1 is 4000. But for year 2 it will be (40000-4000)*10% = 3600 as so on.

One way to solve this can be:

Year 1: 40000 * 0.9 (since we are discounting its value by 10%)
year 2: (40000 * 0.9) * 0.9 = 40000 * (0.9)^2
.
.
.
Year 20: 40000 * (0.9)^20

I hope this helps.

VivekSri · Answer

Hi  tabishkazi

I don't think you need to calculate manually this big calculation, this is very big calculation and retaining will not be easy.

As per mba.com, you can use the calculator. Please read below what they said,

Questions may require math, data analysis, verbal reasoning, or all three. You can use an on-screen calculator while working on this section

tabishkazi · Answer

Thankyou very much. i completely forgot about the calculator.

just incase sombody want to know.

1.09^10 = 1+10c1(0.09)+10c2(0.09)^2 and so on.

we can calculate till here and choose the answer which is little bit bigger than this.

sure if u have calculator no need of all of this.

Sajjad1994 · Answer

Official Explanation

The machine from Company A loses $2,500 of value each year for 15 years, leaving a scrap value of $40,000 – 15($2,500) = $40,000 – $37,500 = $2,500. The machine from Company B loses 10% of its value each year, or seen another way, its value each year is 90% of the previous year’s value. Its scrap value after 20 years is (0.90)20 × $40,000 = $4,863 (and about 7 cents).

pintukr · Answer

A certain piece of equipment is available from two different manufacturers. Either can be purchased for $40,000. The machine from Company A depreciates $2,500 per year and has a life span of 15 years. The machine from Company B loses 10% of its value each year and has a 20-year life span. Find the scrap value of each machine to the nearest dollar.

A. Scrap value of machine from Company A

40000 - (2500 * 15)
= 2500

2500 is the correct answer

B. Scrap value of machine from Company B  
 
40000 ( 1- 10%)^20
= 40000 ( 1- 0.1)^20
= 4863

4863 is the correct answer

Gemmie · Answer

Scrap value of machine A

40,000 - 2,500 * 15
= 40,000 - 37,500
= 2,500

Scrap value of machine B

40,000 * 0.9^20

0.9^20 = 0.9^16 * 0.9^4

0.9^2 = 0.81 
 0.9^4 = 0.81^2 = 0.6561 
 0.9^8 = 0.6561^2 = 0.4304 
 0.9^{16} = 0.4304^2 = 0.1852

0.9^{16} * 0.9^4 = 0.1852 * 0.6561 = 0.1215

40,000 * 0.1228 = 4860 closest to 4863

NoeticImbecile · Answer

Hello, can you please confirm whether the calculator supports this kind of calculation, which is a number to the power 20 times

Shubham.Sharma · Answer

Hi, I don't think that the provided calculator in Data Insights can perform x^y operation.  KarishmaB   GMATNinja , can you please guide on how to perform these type of calculations?

KarishmaB · Answer

Multiply 40,000 with .81 ten times or .729 six times and then .81.

bhanu29 · Answer

You can also use calculator
0.9*0.9 = 0.81
then 0.81^10 is
press "0.81" once and "X" then click "=" 10 times u'll have the answer.. (It's quicker because u only enter one operand and an operator then just press =)

maheshdrag · Answer

Hey  pudu ,

The remaining value is dynamic i.e

First Year

Initial Amount:  40000 
10%: 4000

remaining:  36000 
In the 
 In the second year,  we take 10% of  36,000 i.e 3600

pappal · Answer

thanks tabishkazi, even i forgot about calculator

Adit_ · Answer

KarishmaB   Bunuel   bb 
The question says depreciates every year and it usually starts from the end of the year you bought moving on to the next year, without mentioning of when exactly it was bought.
So the depreciation technically starts from 2nd year onwards and since lifespan is 15 year it depreciates for only 14 years right?
Then 40000-2500*14=5000 could be an interpretation imo which is what I chose as well.

Bunuel · Answer

No. On these problems, “depreciates $2,500 per year and has a life span of 15 years” is read as 15 full years of depreciation over its life, meaning you apply the $2,500 reduction 15 times.

Your “starts in the 2nd year so only 14 years” interpretation would require the problem to explicitly say something like “no depreciation during the first year” or “depreciation begins after the first year,” which it does not.

So your $5,000 logic is based on an extra timing assumption that the question never gives.

pappal · Answer

instead using calculator for 0.9^20, its better to use for 0.6561^5

A certain piece of equipment is available from two different manufactu

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Scrap value of machine from Company A	Scrap value of machine from Company B
		$1,783
		$2,500
		$3,284
		$4,000
		$4,863
		$5,000

GMAT Two-part Analysis (TPA) Questions

A certain piece of equipment is available from two different manufactu

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards