Calculate proportional changes using a multiplier
Note: This question is most likely going to be in the calculator exam, so get your calculator ready and let's get started!
David wants to sell his car, his friend Michael told him that for every year David has owned his car the value of the car decreased by 2%. David has owned his car for 5 years! How much is his car now worth if he originally bought his car for £4,000?
If you have a question like this in your exam the first thing you must do is highlight the important facts from the question which will help you find your answer, as I have down above.
Ok, so to find our answer we must firstly acknowledge that it won't be simply an overall 10% decrease, but rather it will go down by 2% of £4000 the first year then the next year it will go down by 2% of £3920 the second year and so on and so forth.
So for the first year we want to decrease the value of the car by 2% so that we are left with 98% of the original value of the car, which is £4000. To find out 98% of £4000 we must first find our multiplier!
For this example our multiplier will be 0.98 so that we can get the value of the car down to 98% of the original price for the first year and the following years there after.
In your calculator enter the following sum:
4000 x 0.98^{5 }= 3,615.68
By using ^{5 }the calculator has worked out each year's decrease from the previous year's new value, thus calculating all 5 years worth of decreases for us at once. Leaving us with our final answer of £3, 615.68
As you can see from above the new value of the car is not simply 10% of the original at £3600, but rather it is £3,615.68 which is just a bit more. By using a multiplier we are able to work out year on year decreases accurately, without error.
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