Judy bought a car for £12,000. She bought the car 4 years ago. Each year the car depreciated by 10%. How much was is the car worth now?

First of all remember to never be intimidated by a question. Don't read a question and say "I don't know," start with what you do know. In this case we know that every year the £12,00 initial value dropped by a factor of 0.9 as this represents a 10% decrease. We could, therefore, just times 12,000 by 0.9, then times the answer to that by 0.9 and so on- 4 times over. But if we just think that in one equation this would be 12,000 x 0.9 x0.9 x0.9 x0.9 we can easily see that this is the same as saying 12,000 X 0.9^4. Punching this into the calculator gives the answer of £7,873.20. Now, this may seem like a slightly long winded way to get to the answer but the theory can be applied to more complex questions where we would not have time to do all of the separate calculations or in questions where we would need to work backwards. For example, a question might say that after 4 years of 10% depreciation the car was worth £7,873.20, how much was it worth originally? Now we can see that to work this out all we have to do is divide 7873.20 by 0.9^4. This gives us the original value of £12,000