A shop trying to sell a laptop reduces its price by 7% at the very end of each week, from an initial price of £600. If you have £365 to spend, how many weeks must you wait until you can buy the laptop?

This is a simple question, but it's important to not get confused when thinking about how the laptop's price gets reduced. We know the price starts at £600, and that it goes down by 7% each week. If something loses 7% of its value, it would then have 93% of its original value. We can therefore multiply £600 by 0.93 to find the laptop's value after one week, which is £558. However, the next price reduction is 7% of £558, not 7% of £600. We can therefore see that the laptop loses less value every week, although the percentage of its value it loses is constant. After 1 week the laptop will have the value of £600 x 0.93¹, after two weeks £600 x 0.93², and so on. We have £365 to spend, so to see how long it will take for the laptop to have this value, we set up the equation £365 = £600 x 0.93^x , where x is the time passed from the start. This can be easily solved to get a value of x = 6.85 weeks. Since the discount is applied at the end of each week, we have to round this number up to the next integer, which would make the 7 the number of weeks we'd have to wait.