Question

Dan buys a car for £3200.

It depreciates at a rate of 5.1% per year.
How much will it be worth in 4 years?
Give your answer to the nearest penny where appropriate.

Answer 1

Using the formula for exponential decay, the car bought by Dan for £3200, with a depreciation rate of 5.1% per year, will be worth approximately £2610.24 after 4 years.

Step-by-step explanation:

Dan buys a car for £3200, and it depreciates at a rate of 5.1% per year. To find out how much it will be worth in 4 years, we use the formula for exponential decay, which is final value = initial value × (1 - rate of depreciation)^number of years. Here, the rate of depreciation is 5.1% or 0.051 as a decimal. The calculation is as follows:

1. Convert the percent to a decimal: 5.1% = 0.051
2. Subtract the rate from 1: 1 - 0.051 = 0.949
3. Raise this to the power of 4, as the car is depreciating over 4 years: 0.949^4 ≈ 0.8157
4. Multiply the initial value by this decay factor: £3200 × 0.8157 ≈ £2610.24

Therefore, after 4 years, the car will be worth approximately £2610.24 to the nearest penny.