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805+ Level|   Math Related|      
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Sajjad1994
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Mike is considering job offers from two competing firms. Acme Anvils 01 Nov 2023, 10:55
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Salary in year 20 with Acme Anvils: $126,348 Salary in year 20 with Retro Rockets: $117,000
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95% (hard)

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36% (02:48) correct 64% (02:44) wrong based on 317 sessions

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Data Insights (DI) Butler 2023-24 [Question #81, Date: Oct-31-2023] [Click here for Details]

Mike is considering job offers from two competing firms. Acme Anvils offers an annual salary of $50,000 with a guaranteed increase of 5% every year. Retro Rockets offers an annual salary of $60,000 with a $3,000 increase each year. Find the salary Mike can expect to earn after 20 years with each company.
Salary in year 20 with Acme Anvils Salary in year 20 with Retro Rockets
$97,500
$117,000
$121,750
$126,348
$132,665
$151,617
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Salary in year 20 with Acme Anvils: $126,348 Salary in year 20 with Retro Rockets: $117,000
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soumyap09
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Mike is considering job offers from two competing firms. Acme Anvils 02 Nov 2023, 13:44
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Please explain how Acme Anvil salary is 126,348
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YashM_10
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Mike is considering job offers from two competing firms. Acme Anvils 03 Nov 2023, 07:27
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soumyap09
Please explain how Acme Anvil salary is 126,348

For finding out Acme Anvil salary it says that there is a fixed increase of 5% every year. It is similar to a compounding of 50,000 at an interest rate of 5%.
Now to find the time period for a period of 20 years in the company the number of raise is going to be for 19 years as for the first year there is no raise.

so final amount = 50000*(1.05)^19 = 126,347.5. I would have used a calculator to get to this value where I would have squared 1.05 four time to get 1.05^16 and then get to 19.

If anyone has a better solution to find value of 1.05^19 without using calculation please help.
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Mike is considering job offers from two competing firms. Acme Anvils 04 Nov 2023, 08:18
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even i have the same question how to calculate 1.05^19 fast.
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Mike is considering job offers from two competing firms. Acme Anvils 06 Nov 2023, 08:46
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tabishkazi
even i have the same question how to calculate 1.05^19 fast.

Please keep in mind that this is the DI section, and you can use the calculator here. There is no need to calculate it manually.

Best.
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Mike is considering job offers from two competing firms. Acme Anvils 06 Nov 2023, 08:47
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Official Explanation

If Mike accepts the offer from Acme Anvils, his year 20 salary will reflect 19 increases of 5% and will be $50,000 × 1.0519 = $126,347.51. If he takes the job with Retro Rockets, he will have received 19 raises of $3,000 each, and his salary will be $60,000 + 19 × $3,000 = $117,000.
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Mike is considering job offers from two competing firms. Acme Anvils 17 Feb 2024, 20:23
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­Why 19 ?? why is salary after 1st year not changing.
If the question had been find salary after 1 year, would it still have remained same with no increment ???
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Mike is considering job offers from two competing firms. Acme Anvils 17 Feb 2024, 21:25
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dazzler97
­Why 19 ?? why is salary after 1st year not changing.
If the question had been find salary after 1 year, would it still have remained same with no increment ???
­
Suppose Person Joined the company on 1st January 2023. 
On December 31st 2023, he will complete 1 year and will get the annual salary of $60,000
Salary at the end of 1 year or after 1 year is $60,000.
Yes salary after 1st year would be without the increment.

Salary at the end of 2 year on December 31st 2024( or after 2 year of joining) will be $60,000+$3000 Bonus
Increment in the salary will only be after 2 year onwards. 

 ­
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Mike is considering job offers from two competing firms. Acme Anvils 03 Mar 2024, 14:52
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tabishkazi
even i have the same question how to calculate 1.05^19 fast.

Please keep in mind that this is the DI section, and you can use the calculator here. There is no need to calculate it manually.

Best.
­Hi 
Indeed, there is a calculator available in the DI section. However, it is a very basic one and there is no square function or any exponent function there. So depsite the fact that there is a calculator, which would definiely make the "final" calculation of 50,000 * 2.526 (=1.05^19) a lot easier, I have no idea how to get the value of 2.526 i.e. 1.05^19 in the first place (obviously entering 1.05*1.05*1.05..... 19 times is out of question for me as it would cost me way too much time). Would you know how we can leverage the calculator to get the approximate value of 1.05^19?

Many thanks.­
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Mike is considering job offers from two competing firms. Acme Anvils 06 Mar 2024, 12:24
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Laracbo
Sajjad1994
tabishkazi
even i have the same question how to calculate 1.05^19 fast.

Please keep in mind that this is the DI section, and you can use the calculator here. There is no need to calculate it manually.

Best.
­Hi 
Indeed, there is a calculator available in the DI section. However, it is a very basic one and there is no square function or any exponent function there. So depsite the fact that there is a calculator, which would definiely make the "final" calculation of 50,000 * 2.526 (=1.05^19) a lot easier, I have no idea how to get the value of 2.526 i.e. 1.05^19 in the first place (obviously entering 1.05*1.05*1.05..... 19 times is out of question for me as it would cost me way too much time). Would you know how we can leverage the calculator to get the approximate value of 1.05^19?

Many thanks.­
­Vous Utilisez votre cerveau (1.05)^4 = 1.215 alors mutlipliez 1.215 cinq fois i.e 1.215*5/1.05 = (1.05)^19
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Mike is considering job offers from two competing firms. Acme Anvils 30 May 2024, 02:00
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­Salary in year 20 with Acme Anvils: \(50 * 1.05^{19}\)

\(1.05^{19} = (1.05^4)^4 * 1.05^{3}\)

\(1.05^4 = 1.2155\)
\(1.2155^4 = 2.183\)
\(2.18 * 1.05 * 1.05 * 1.05 = 2.527\)

50 * 2.527 = 12.6.35

==> 126,348


Salary in year 20 with Retro Rockets: 60k + 3k * 19 = 117k

==> 117,000

 ­
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