Question

Mrs. Johnson paid $17,500 for a used car 3 years ago. Because she did not properly maintain the car, she sold it for only $4,500. What was the rate of depreciation to thenearest whole percent?25%20%15%45%None of these choices are correct.

Answer 1

The formula to be used for calculating depreciation is given by;

`\begin{gathered} \text{salvage value = Original cost \lbrack{}1-}\frac{depreciation\text{ rate}}{100}\rbrack^{\text{time}}^{} \\ \text{where;} \\ \text{salvage value = \$4,500} \\ \text{original cost = \$17,500} \\ \text{time = 3years} \end{gathered}`

Substituting all these in the formula above and making the rate the subject of the formula, we have

`\begin{gathered} 4500=17500\lbrack1-(r)/(100)\rbrack^3 \\ (4500)/(17500)=\lbrack1-(r)/(100)\rbrack^3 \\ 0.2571=\lbrack1-(r)/(100)\rbrack^3 \\ \sqrt[3]{0.2571}=\lbrack1-(r)/(100)\rbrack \\ 0.6359=\lbrack1-(r)/(100)\rbrack \\ (r)/(100)=1-0.6359 \\ (r)/(100)=0.3641 \\ \text{cross multiplying, we have} \\ r=0.3641*100 \\ r=36.41\text{ \%} \end{gathered}`

Hence, the rate of depreciation to the nearest whole percent is 36%

Therefore, none of the choices given are correct.