A new phone cost £679The value of the phone decreases at a rate of 4% per year.Work out the value of the phone at the end of 3 years.

Step 1: Understand the problem The problem is asking for the value of the phone after 3 years, given that it decreases in value by 4% each year.

Step 2: Calculate the annual depreciation To find the value of the phone after each year, we need to subtract 4% of its value. Since the phone is worth £679 at the start, the depreciation for the first year is 4% of £679.

Step 3: Calculate the value after the first year To find the value of the phone after the first year, subtract the depreciation from the initial value.

Step 4: Repeat steps 2 and 3 for the next two years The value of the phone after the second year is found by subtracting 4% of the value after the first year. The value after the third year is found by subtracting 4% of the value after the second year.

Let's do the calculations:

Year 1: 4% of £679 = £27.16 £679 - £27.16 = £651.84

Year 2: 4% of £651.84 = £26.07 £651.84 - £26.07 = £625.77

Year 3: 4% of £625.77 = £25.03 £625.77 - £25.03 = £600.74

So, the value of the phone at the end of 3 years is £600.74.

To calculate the value of the phone at the end of 3 years, we need to apply the annual depreciation rate of 4% to the initial cost of the phone for each of the 3 years.

Here are the steps:

1. Convert the depreciation rate from a percentage to a decimal by dividing by 100. So, 4% becomes 0.04.

2. Subtract this rate from 1 to find the annual depreciation multiplier. So, 1 - 0.04 = 0.96. This means that each year, the phone retains 96% of its value from the previous year.

3. Multiply the initial cost of the phone by the annual depreciation multiplier for each year.

Year 1: £679 * 0.96 = £652.04 Year 2: £652.04 * 0.96 = £626.36 Year 3: £626.36 * 0.96 = £601.30

So, the value of the phone at the end of 3 years is approximately £601.30.