(a) The value of a , b , c , d , e and f .

Question

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Answer 1

Question

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

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Answer 2

Question

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

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Answer 3

Question

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

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Answer 4

Question

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

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Answer 5

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Answer 6

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Answer 7

Chapter 14, Problem 65P

To determine

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

Answer 8

Expert Solution

Answer to Problem 65P

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Concept used:

Write the expression for annual percentage increase in $nth$ year.

$(Annual % increase in nth year)=(MSIn−MSIn-1MSIn-1)×100$ ...... (I)

Here, manager’s salary index of the year is $MSIn$ and the manager’s salary index of the previous year is $MSIn-1$ .

Write the expression for $MSI$ in any year.

$MSIn=MSIn-1+(change in MSI%(MSIn-1))$ ...... (II)

Calculations:

Calculate the annual percentage increase in $2009$ .

Substitute $100$ for $MSI2009$ and $93$ for $MSI2008$ in Equation (I).

$Annual % increase in year 2009=(100−9393)×100=7.52%$

The value of $a$ is $7.52%$ .

Calculate the $MSI$ in year $2010$ .

Substitute $100$ for $MSI2009$ and $5%$ for change in $MSI%$ in Equation (II).

$MSI2010=100+5%(100)=100+5=105$

The value of $b$ is $105$ .

Calculate the annual percentage increase in $2011$ .

Substitute $115$ for $MSI2011$ and $105$ for $MSI2010$ in Equation (I).

$Annual % increase in year 2011=(115−105105)×100=9.5%$

The value of $c$ is $9.5%$ .

Calculate the annual percentage increase in $2012$ .

Substitute $126$ for $MSI2012$ and $115$ for $MSI2011$ in Equation (I).

$Annual % increase in year 2012=(126−115115)×100=9.6%$

The value of $d$ is $9.6%$ .

Calculate the $MSI$ in year $2013$ .

Substitute $126$ for $MSI2012$ and $1.2%$ for change in $MSI%$ in Equation (II).

$MSI2013=126+1.2%(126)=126+2=128$

The value of $e$ is $128$ .

Calculate the $MSI$ in year $2016$ .

Substitute $145$ for $MSI2015$ and $12%$ for change in $MSI%$ in Equation (II).

$MSI2016=145+12%(145)=145+17=162$

The value of $f$ is $162$ .

Conclusion:

The value of $a$ is $7.52%$ .

The value of $b$ is $105$ .

The value of $c$ is $9.5%$ .

The value of $d$ is $9.6%$ .

The value of $e$ is $128$ .

The value of $f$ is $162$ .

Answer 13

To determine

(b)

The base year of $MSI$ .

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

Answer 14

To determine

(b)

The base year of $MSI$ .

Answer 15

Expert Solution

Answer to Problem 65P

The base year of $MSI$ is $2009$ because it has an index value of $100$ .

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The base value is taken as $100$ and the year in which value is $100$ is deemed to be a base year. There is always a year called as base year among all index having value of $100$ .

The base year of $MSI$ is $2009$ because it has index value of $100$ .

Answer 20

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Answer 21

To determine

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

Answer 22

Expert Solution

Answer to Problem 65P

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Answer 23

Expert Solution

Answer 24

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculations:

The table for average increase in salaries from $2009$ to $2013$ is shown below.

Year	MSI	Change in MSI
$2009$	$100$	$7.52%$
$2010$	$105$	$5%$
$2011$	$115$	$9.5%$
$2012$	$126$	$9.5%$
$2013$	$128$	$1.2%$
Average		$32.82%5=6.56%$

Table (1)

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The table for average increase in salaries from $2013$ to $2017$ is shown below.

Year	MSI	Change in MSI
$2013$	$128$	$1.2%$
$2014$	$138$	$8.30%$
$2015$	$145$	$5.10%$
$2016$	$162$	$12%$
$2017$	$170$	$4.5%$
Average		$31.1%5=6.22%$

Table (2)

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Conclusion:

The average annual price increase in salaries from $2009$ to $2013$ is $6.56%$ .

The average annual price increase in salaries from $2013$ to $2017$ is $6.22%$ .

Answer 27

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Answer 28

To determine

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .

Answer 29

Expert Solution

Answer to Problem 65P

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Answer 30

Expert Solution

Answer 31

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculations:

Calculate the $MSI$ in year $2018$ .

Substitute $170$ for $MSI2017$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2017=170+(6.56%(170))=170+11=181$

The $MSI$ in year $2018$ is $181$ .

Calculate the $MSI$ in year $2019$ .

Substitute $181$ for $MSI2018$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=181+(6.56%(181))=181+12=193$

The $MSI$ in year $2019$ is $193$ .

Calculate the $MSI$ in year $2020$ .

Substitute $193$ for $MSI2019$ and $6.56%$ for change in $MSI%$ in Equation (II).

$MSI2019=193+(6.56%(193))=193+13=206$

The $MSI$ in year $2020$ is $206$ .

Conclusion:

The $MSI$ in year $2018$ is $181$ .

The $MSI$ in year $2019$ is $193$ .

The $MSI$ in year $2020$ is $206$ .

Answer 34

Ch. 14 - Prob. 1QTC Ch. 14 - Prob. 2QTC Ch. 14 - Prob. 3QTC Ch. 14 - Prob. 4QTC Ch. 14 - Prob. 1P Ch. 14 - Prob. 2P Ch. 14 - Prob. 3P Ch. 14 - Prob. 4P Ch. 14 - Prob. 5P Ch. 14 - Prob. 6P

(a) The value of a , b , c , d , e and f .

(a) The value of a<m:math><m:mi>a</m:mi></m:math>, b<m:math><m:mi>b</m:mi></m:math>, c<m:math><m:mi>c</m:mi></m:math>, d<m:math><m:mi>d</m:mi></m:math>, e<m:math><m:mi>e</m:mi></m:math> and f<m:math><m:mi>f</m:mi></m:math>.

Answer to Problem 65P

Explanation of Solution

(b) The base year of MSI<m:math><m:mrow><m:mtext>MSI</m:mtext></m:mrow></m:math>.

Answer to Problem 65P

Explanation of Solution

(c) The average annual price increase in salaries from 2009<m:math><m:mrow><m:mn>2009</m:mn></m:mrow></m:math> to 2013<m:math><m:mrow><m:mn>2013</m:mn></m:mrow></m:math> and 2013<m:math><m:mrow><m:mn>2013</m:mn></m:mrow></m:math> to 2017<m:math><m:mrow><m:mn>2017</m:mn></m:mrow></m:math>.

Answer to Problem 65P

Explanation of Solution

(d) The MSI<m:math><m:mrow><m:mtext>MSI</m:mtext></m:mrow></m:math> in year 2018<m:math><m:mrow><m:mn>2018</m:mn></m:mrow></m:math>, 2019<m:math><m:mrow><m:mn>2019</m:mn></m:mrow></m:math> and 2020<m:math><m:mrow><m:mn>2020</m:mn></m:mrow></m:math>.

Answer to Problem 65P

Explanation of Solution

Want to see more full solutions like this?

Chapter 14 Solutions

(a)

The value of $a$ , $b$ , $c$ , $d$ , $e$ and $f$ .

(b)

The base year of $MSI$ .

(c)

The average annual price increase in salaries from $2009$ to $2013$ and $2013$ to $2017$ .

(d)

The $MSI$ in year $2018$ , $2019$ and $2020$ .