The value of a new car is £18000. 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.
In the 1st year the car loses 25% of its value, meaning it retains 75% of its value. The starting value (100%) was £18000, so multiplying this by the 75% retained - remembering to change this to decimal notation, gives the new value. 18000 * 0.75 = 13500.
In the next 4 years the car loses 12% of its value each year, meaning it retains 88% of the value from the previous year. The starting value before these 4 years is £13500, remembering it has already lost 25% of the original value by this point. For each year this needs to be multiplied by the 88% retained - as there are 4 years it loses this value it will be multiplied by 88% 4 times.13500 * 0.88 * 0.88 * 0.88 * 0.88 This can be simplified to 13500 * (0.88)4 = £8095.89 Notice how when the value decreases the same amount in consecutive time periods (years), the equation to solve the question takes the form Starting value * (Value retained)Number of times This holds true when the value is increasing too.
