Chapter 15, Problem 2PA

Summary Introduction

(a)

To determine:

The annual needs of G in today’s dollars.

Introduction:

Annual needs means the amounts needs to spent on current expenses of the individual. An individual not only think for the present need but also consider the future needs and that is the reason they invest amount in retirement plans.

Explanation of Solution

Given,

Current salary is $50,000.

The formula to calculate annual needs is,

$\text{Annual needs}=\text{Current salary}\times 90\%$

Substitute $50,000 for current salary in the above formula.

$\begin{array}{c}\text{Annual needs}=\$50,000\times 90\%\\ =\$45,000\end{array}$

The annual need is $45,000.

Conclusion

Thus, the annual needs of G after retirement are $45,000.

Summary Introduction

(b)

To determine:

The annual requirement of G in today’s dollars with the effect of taxes

Explanation of Solution

Given,

Annual need is $45,000 as calculated in part a.

Average tax rate is 14% at the time of retirement.

The formula to calculate the annual requirement is,

$\text{Annual requirement}=\frac{\text{Annual needs}}{\left(1-\text{Tax rate}\right)}$

Substitute $45,000 for annual needs and tax rate is 14% in the above formula.

$\begin{array}{c}\text{Annual requirement}=\frac{\$45,000}{\left(1-0.14\right)}\\ =\frac{\$45,000}{0.86}\\ .=\$52,325.58\end{array}$

Conclusion

Thus, the annual requirement after adjusting for tax is $52,325.58.

Summary Introduction

(c)

To determine:

The annual requirement of G in future dollars with the effect of inflation.

Explanation of Solution

Given,

The annual requirement after adjusting for tax is $52,325.58 as calculated in part b.

The retirement of G is in 40 years

The inflation rate is 3%

The formula to calculate the annual requirement is,

$\text{Annual requirement}=\text{Annual need after taxes}\times {\left(1+\text{inflation rate}\right)}^{40}$

Substitute $52,325.58 for annual need after taxes and inflation rate is 3% in the above formula.

$\begin{array}{c}\text{Annual requirement}=\$52,325.58\times {\left(1+0.03\right)}^{40}\\ =\$52,325.58\times {\left(1.03\right)}^{40}\\ =\$52,325.58\times 3.262\\ =\$170,686.04\end{array}$

Conclusion

Thus, the annual need after adjusting for inflation is $170,686.04.

Summary Introduction

(d)

To determine:

The total requirement if the age of retirement of G is 20 years.

Explanation of Solution

Given,

The annual need after adjusting for inflation is $170,686.04 as calculated in part c.

The retirement of G is in 20 years

The inflation adjusted rate of return is $\left(8\%-3\%\right)=5\%$

The present value interest factor annuity (PVIFA) of 5% for 20 years is 12.46.

The formula to calculate total requirement is,

$\text{Total requirement}=\text{Annual needs}\times \text{PVIFA factor}$

Substitute $170,686.04 for annual needs and 12.46 for PVIFA in the above formula.

$\begin{array}{c}\text{Total requirement}=\$170,686.04\times 12.46\\ =\$2,126,748.05\end{array}$

Conclusion

Thus, the total requires amount needed for retirement is $2,126,748.05.

Summary Introduction

(e)

To determine:

The total amount of monthly saving done by G.

Explanation of Solution

Given,

Total requirement as calculated in part d is $2,126,748.05

The future value interest factor annually (FVIFA) at 8% for 40 years is 295.02.

The formula to calculate monthly saving is,

$\text{Monthly saving}=\frac{\frac{\text{Total needs}}{\text{FVIFA}}}{12}$

Substitute $2,126,748.05 for total needs and 295.02 for FVIFA in the above formula.

$\begin{array}{c}\text{Monthly saving}=\frac{\frac{\$2,126,748.05}{295.02}}{12}\\ =\frac{\$7,208.83}{12}\\ =\$600.74\end{array}$

Conclusion

Thus, G must save $600.74 monthly to meet his retirement needs.