Question

The value of a car is depreciating at a rate of 5% per year. In 2010, the car was worth $32,000. Find the value of the car in 2013.step 1: decide whether it is growing or decaying:step 2: solve for the rate:step 3: solve:

Answer 1

Data:

Depreciating: The value decrease

Rate: 5% per year

2010: $32,000

2013: $?

Step 1: As depreciating means decrease, the value of the car is decaying

Step 2 and step 3: You use the formula below to find the value of the car after 3 years (as the value is decaying the rate in the formula is substracting)

Final value: F

Principal value: P=32000

rate: r=5

Time in years: n=3 (2013-2010=3)

$\begin{gathered} F=P(1-\frac{r}{100})^n \\ \\ F=32000(1-\frac{5}{100})^3 \\ \\ F=32000(0.95)^3 \\ \\ F=27436 \end{gathered}$

In 2013 the value of the car is $27,436