Chapter 6, Problem 1P

To determine

Calculate the annual worth.

Explanation of Solution

Time period is denoted by n and interest rate is denoted by i. Annual worth (Aw) can be calculated as follows.

$\begin{array}{c}\text{AW}\left({\text{CF}}_0+\frac{{\text{CF}}_1}{{\left(1+\text{i}\right)}^{\text{1}}}+\frac{{\text{CF}}_2}{{\left(1+\text{i}\right)}^{\text{2}}}+\mathrm{...}+\frac{{\text{CF}}_{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}}\right)\left(\frac{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{n}}}{{\left(\text{1}+\text{i}\right)}^{\text{n}}-\text{1}}\right)\\ =\left(\begin{array}{l}300+\frac{100}{{\left(1+0.1\right)}^1}+\frac{-160}{{\left(1+0.1\right)}^2}+\frac{150}{{\left(1+0.1\right)}^3}\\ +\frac{200}{{\left(1+0.1\right)}^4}+\frac{200}{{\left(1+0.1\right)}^5}+\frac{130}{{\left(1+0.1\right)}^6}\end{array}\right)\left(\frac{0.1{\left(1+0.1\right)}^6}{{\left(1+0.1\right)}^6-1}\right)\\ =24.23\end{array}$

Annual worth is $24.43.