Question

A car costing $25 000 depreciates 30% of its value each year. What is the new value at the end of 3 years?

Answer 1

To calculate the value of a car after it depreciates by 30% each year, we can use the formula for depreciation:

\[
\text{Value after } n \text{ years} = \text{Initial Value} \times (1 - \text{depreciation rate})^n
\]

Given:
- Initial Value = $25,000
- Depreciation rate = 30% = 0.30
- \( n = 3 \) years

Substituting in the values:

\[
\text{Value after 3 years} = 25000 \times (1 - 0.30)^3
\]
\[
= 25000 \times (0.70)^3
\]
\[
= 25000 \times 0.343
\]
\[
\approx 25000 \times 0.343 = 8575
\]

Thus, the new value of the car at the end of 3 years is approximately **$8,575**.