[Solved]The value of a new car is £18,000. The value of the car decreases by 25% in the first year and 12% in each of the next 4 years. Work out the value of the car after 5 years.

Solution: From the question, it is given that the value of a new car is £18,000.

The value of car decreased by 25% in the first year.

Now we will find the value of the car after it decreased by 25%

25% of 18000=£4500

Value of car after it decreased by 25% = Initial value – Decreased value

Value of the car after it decreased by 25% = 18000 – 4500

Value of the car after it decreased by 25% = 13500

In the next 4 years, the car loses 12% of its value each year, which means it retains 88% of the value from the previous year.

Starting value before these 4 years = £13500

The car has already lost 25% of its original value.

Now, for each year, this needs to be multiplied by the 88% retained because there are Four years.

As it loses this value, it will be multiplied by 88% 4 times.

13500×0.88×0.88×0.88×0.88

13500×(0.88)⁴

13500×0.59969536

£8095

Hence, the value of the car after five years is £8095.

Conclusion

The value of a new car is £18,000. The car’s value decreases by 25% in the first year and 12% in the next 4 years. the value of the car after five years is £8095.