Comound interest: A car is bought for the price of £12 000, but its value depreciates every year by 8%. Calculate, how much will the car be worth in 5 years
The question states the value of the car depreciates every year by 8%. This means that from the original, 100% value of the car in a set year, every consecutive year the value will decrease by 8% so that the value of the car in the next year will be 92% the value of the original price in the first year. As a result, to find the value of the car in the next year, we deduce 8% from 100% and multiply it by 12000. We express 100% as 100/100 (=1) and 8% as 8/100 (=0.08) to facilitate calculations. In one year, the value of the car will be 12000 x (1 - 8/100), in other words, 12000 x 0.92, which equals 11040.Consequently, after the second year, to calculate the value, we take the cost of the car after one year and do the same: 11040 x 0.92We then repeat this 5 times. However, to avoid long calculations (as it is 5 years), we can simplify this by introducing the power of 5.We now take the original value of the car and multiply it by 0.92 which is also to the power of 5.12000 x (1 - 8/100)5 = 7908.978278 (or 7908.98 rounded to two decimal places)
