Chapter 4, Problem 61QP

1.

Summary Introduction

To compute: The present value of two years back pay.

Purchasing Power:

It refers to the ability of the person to buy something. Purchasing power decreases with an increase in inflation and increase with the decrease in inflation.

Explanation of Solution

Salary 2 years back is $37,000.

Annual rate of interest is 7.56% (working note).

EAR is 7.80%.

Monthly salary of previous year is $39,000.

Formula to calculate the future value,

$\text{Future}\text{value}=\text{Monthly}\text{salary}\times \frac{{\left(1+\text{rate}\text{of}\text{interest}\right)}^{\text{Time}}-1}{\text{rate}\text{of}\text{interest}}\times \left(1+\text{EAR}\right)$

Substitute $37,000 divided by 12 for monthly salary, 7.56% for rate of interest and 12 months for time and 7.8% for EAR.

$\begin{array}{c}\text{Future}\text{value}=\frac{\$37,000}{12}\times \frac{{\left(1+0.00756\right)}^{12}-1}{0.00756}\times \left(1+0.078\right)\\ =\$38,878.80\end{array}$

Hence, the present value of salary 2 years back is $38,878.80.

Substitute $39,000 divided by 12 for monthly salary, 0.63% for rate of interest and 12 months for time.

$\begin{array}{c}\text{Future}\text{value}=\frac{\$39,000}{12}\times \frac{{\left(1+0.00756\right)}^{12}-1}{0.00756}\\ =\$40,663.19\end{array}$

Hence, the present value of salary 1 year back is $40,663.19.

2.

Summary Introduction

To compute: The present value of five years future salary.

Explanation of Solution

Given,

Monthly salary is $43,000.

Formula to calculate the present value of next 5 years,

$\text{Present}\text{value}=\text{Monthly}\text{salary}\times PVIF{A}_{0.63\%,5\text{years}\times 12\text{months}}$

Substitute $43,000 for monthly salary and 49.834,

$\begin{array}{c}\text{Present}\text{value}=\frac{\$43,000}{12}\times 49.834\\ =\$3,583.33\times 49.834\\ =\$178,571.67\end{array}$

Hence, the present value of next 5 years is $178,571.67.

3.

Summary Introduction

To calculate: The total amount paid to plaintiff.

Explanation of Solution

Given,

Suffering expenses is $150,000.

Court expenses are $25,000.

Formula to calculate the total amount paid to plaintiff,

$\text{Total}\text{amount}=\left(\begin{array}{l}\text{Present}\text{value}\text{of}2\text{years}\text{}\text{back}+\text{Present}\text{value}\text{of}\text{1}\text{year}\text{}\text{back}\\ +\text{Present}\text{value}\text{of}\text{next}5\text{years}+\text{Suffering}\text{expenses}\\ +\text{Court}\text{expenses}\end{array}\right)$

Substitute $41,152.33 for the present value of 2 years back, $40,238.25 for the present value of 1 year back, $178,571.67 for the present value of next 5 years, $150,000 for suffering expenses and $25,000 for court expenses.

$\begin{array}{c}\text{Total}\text{amount}=\$41,152.33+\$40,238.25+\$178,571.67+\$150,000+\$25,000\\ =\$434,962.25\end{array}$

Hence, the total amount paid to plaintiff is $434,962.25.

Working note:

Computation of the annual percentage rate,

$\begin{array}{c}\text{EAR}={\left(1+\frac{\text{Annual}\text{percentage}\text{rate}}{\text{Compounding}\text{periods}}\right)}^{\text{Compounding}\text{periods}}-1\\ 7.8\%={\left(1+\frac{\text{Annual}\text{percentage}\text{rate}}{12}\right)}^{12}-1\\ \text{Annual}\text{percentage}\text{rate}=0.0063\times 12\\ =7.56\%\end{array}$

Hence, annual percentage rate is 7.56%.

Therefore, the lower rate of interest would be preferred by the plaintiff as to get the lowering of the future value.

Conclusion

Hence, the total amount paid to plaintiff is $434,962.25.