Chapter 30, Problem 1WNG

(a)

To determine

Calculate the present value.

Explanation of Solution

The present value (PV) can be calculated using the formula given below:

$\text{PV}={\displaystyle \sum \frac{{\text{A}}_{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}}}$        (1)

Here

${\text{A}}_{\text{n}}$ is the actual amount of income.

 i is the interest rate.

n is the number of years in the future.

Since ${\text{A}}_{\text{n}}$ is $25,000, i is 7%, and n is 4 years, the value of PV can be calculated using Equation-1 as follows:

$\begin{array}{c}\text{PV}=\frac{\$25,000}{{\left(1+0.07\right)}^1}+\frac{\$25,000}{{\left(1+0.07\right)}^2}+\frac{\$25,000}{{\left(1+0.07\right)}^3}+\frac{\$25,000}{{\left(1+0.07\right)}^4}\\ =\$23,364.49+\$21,835.976+\$20,407.45+\$19,072.38\\ =\$84,680.28\end{array}$

Thus, PV is $84,680.28.

Economics Concept Introduction

Present value: The present value measures the value today of a future cash flow or a series of cash flows.

(b)

To determine

Calculate the present value.

Explanation of Solution

Since ${\text{A}}_{\text{n}}$ is $152,000, i is 6%, and n is 5 years, the value of PV can be calculated using Equation-1 as follows:

$\begin{array}{c}\text{PV}=\frac{\$152,000}{{\left(1+0.06\right)}^1}+\frac{\$152,000}{{\left(1+0.06\right)}^2}+\frac{\$152,000}{{\left(1+0.06\right)}^3}+\frac{\$152,000}{{\left(1+0.06\right)}^4}+\frac{\$152,000}{{\left(1+0.06\right)}^5}\\ =\$143,396.2+\$135,279.5+\$127,622.1+\$120,398.2+\$113,583.2\\ =\$640,279.3\end{array}$

Thus, PV is $640,279.3.

(c)

To determine

Calculate the present value.

Explanation of Solution

Since ${\text{A}}_{\text{n}}$ is $60,000, i is 6.5%, and n is10 years, the value of PV can be calculated using Equation-1 as follows:

$\begin{array}{c}\text{PV}=\frac{\$60,000}{{\left(1+0.065\right)}^1}+\frac{\$60,000}{{\left(1+0.065\right)}^2}+\frac{\$60,000}{{\left(1+0.065\right)}^3}+\frac{\$60,000}{{\left(1+0.065\right)}^4}+\frac{\$60,000}{{\left(1+0.065\right)}^5}\\ +\frac{\$60,000}{{\left(1+0.065\right)}^6}+\frac{\$60,000}{{\left(1+0.065\right)}^7}+\frac{\$60,000}{{\left(1+0.065\right)}^8}+\frac{\$60,000}{{\left(1+0.065\right)}^9}+\frac{\$60,000}{{\left(1+0.065\right)}^{10}}\\ =\$56,338.03+\$52,899.56+\$49,670.95+\$46,6369.39+\$43,792.85\\ +\$41,120.05+\$38,610.37+\$36,253.87+\$34,041.19+\$31,963.56\\ =\$431,329.8\end{array}$

Thus, PV is $431,329.8.