Question

Amelia buys a car for £15770 which depreciates in value at a rate of

4% per year.
Work out how much Amelia's car will be worth in 14 years

Answer 1

Amelia's car will depreciate according to the formula for exponential decay. After 14 years with a depreciation rate of 4% per year, the car will be worth approximately £8,168.66.

Step-by-step explanation:

To calculate how much Amelia's car will be worth in 14 years, given it depreciates at a rate of 4% per year, we use the formula for exponential decay: final value = initial value × (1 - rate of depreciation)^time.

In this case, the initial value is £15,770, the rate of depreciation is 0.04 (4%), and the time is 14 years.

The final value of Amelia's car after 14 years would be: £15,770 × (1 - 0.04)^14

First, calculate 1 - 0.04 to find the annual depreciation multiplier: 1 - 0.04 = 0.96

Now, raise 0.96 to the power of 14 to find the multiplier after 14 years: 0.96^14 ≈ 0.518

Multiplying this by the initial value gives the final value: £15,770 × 0.518 ≈ £8,168.66

Therefore, Amelia's car will be worth approximately £8,168.66 after 14 years.