Question

Dan buys a car for £2100.

It depreciates at a rate of 2.2% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.

Answer 1

To find the future value of the car after 6 years of depreciation at 2.2% per year, you apply the formula V = P (1 - r)^t, which results in the car being worth approximately £1837.61.

Step-by-step explanation:

To calculate the value of a car after depreciation, we use the formula for exponential decay, which reflects how an asset like a car loses value over time. Dan buys a car for £2100, and it depreciates at a rate of 2.2% per year. The formula to find the future value of the car after depreciation is:

• V = P (1 - r)^t

• where V is the future value of the car, P is the present value (£2100), r is the rate of depreciation (0.022), and t is the time in years (6 years).

Applying these values to the formula, we can calculate the future value of the car:

• V = £2100 (1 - 0.022) ⁶

• V = £2100 (0.978) ⁶

• V = £2100 (0.875)

• V = £1837.61

Therefore, the car will be worth approximately £1837.61 after 6 years, to the nearest penny.