$1$ ) For tax purposes, a car rental company assumes each car in their fleet depreciates by $6 \%$ per year. If the initial value of a car is $\$ 27,700.00$ , what will the value be when the car is $9$ years old?

Full solution

1

) For tax purposes, a car rental company assumes each car in their fleet depreciates by

6 \%

per year. If the initial value of a car is

\$ 27,700.00

, what will the value be when the car is

9

years old?

Calculate Annual Depreciation Rate: Calculate the annual depreciation rate as a decimal. $6\%$ as a decimal is $0.06$ .
Apply Depreciation Formula: Apply the depreciation formula: Final Value = Initial Value $\times$ $(1 - \text{Depreciation Rate})^{\text{Number of Years}}$ . Here, it's $\$27,700 \times (1 - 0.06)^9$ .
Calculate $1 - 0.06$ : Calculate $(1 - 0.06)$ which is $0.94$ .
Calculate $0.94^9$ : Calculate $0.94$ raised to the $9$ th power. $0.94^9 \approx 0.574349$ .
Multiply Initial Value: Multiply the initial value by the result from the previous step: $\$27,700 \times 0.574349 \approx \$15,909.36$ .