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A certain piece of equipment is available from two different manufactu

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Sajjad1994
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A certain piece of equipment is available from two different manufactu [#permalink] New post   02 Nov 2023, 07:32
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Data Insights (DI) Butler 2023-24 [Question #84, Date: Nov-01-2023] [Click here for Details]


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.
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
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Scrap value of machine from Company A: $2,500 Scrap value of machine from Company B: $4,863
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   03 Nov 2023, 08:56
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
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Ash381
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   03 Nov 2023, 22:07
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Sajjad1994 wrote:
Data Insights (DI) Butler 2023-24 [Question #84, Date: Nov-01-2023] [Click here for Details]


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.


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.
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A certain piece of equipment is available from two different manufactu [#permalink] New post   03 Nov 2023, 22:14
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pudu wrote:
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


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.
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   04 Nov 2023, 08:12
how to calculate 0.9^20 fast? if somebody can help me with it.
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   05 Nov 2023, 21:20
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tabishkazi wrote:
how to calculate 0.9^20 fast? if somebody can help me with it.


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
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   05 Nov 2023, 22:41
VivekPrateek wrote:
tabishkazi wrote:
how to calculate 0.9^20 fast? if somebody can help me with it.


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



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.
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   06 Nov 2023, 08:27
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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).
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   17 Nov 2023, 10:15
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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
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Re: A certain piece of equipment is available from two different manufactu [#permalink] New post   23 Apr 2024, 19:39
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­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
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Re: A certain piece of equipment is available from two different manufactu [#permalink]
23 Apr 2024, 19:39
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