a car depreciates at rate of 10%per year.
the car cost £20000 new.
(a) explain why the car wont be worth £16000 after 2 years
(b) show that the car will be worth £16200 after 2 years and find the value of the car after 3 years
(c) describe the type of correlation between the value of the car and age of the car
every year multiply value by 0.90
1 year= 20,000 * .9
2 years 20,000 * .9^2
3 years 20,000 * .9^3
so part (c)
n years 20,000 * .9^n
It is like reverse compound interest, it will not go down 2,000 every year, but only 10% of its MOST RECENT value every year
so 2 years
20,000 * .81 = 16200
3 years 20,000 * .9 * .9 * .9
(c) already did above
thanks Damon
1 THING HOW COME 0.90?
a loss of 10% means that each year the value is 90% of what it was before.
(a) To explain why the car won't be worth £16000 after 2 years, we need to understand how depreciation works. Depreciation is the decrease in the value of an asset over time. In this case, the car depreciates at a rate of 10% per year.
So, after the first year, the car's value would be £20000 - (10% of £20000) = £18000. This means that it has lost £2000 in value.
Now, after the second year, if we apply the same depreciation rate of 10%, we would calculate the depreciation as follows:
£18000 - (10% of £18000) = £16200
Therefore, the car would be worth £16200 after 2 years, not £16000.
(b) We have already determined that the car will be worth £16200 after 2 years. Now, to find the value of the car after 3 years, we can apply the same depreciation rate.
Using the same formula, we'll subtract 10% of the car's value after 2 years (£16200) from the previous value:
£16200 - (10% of £16200) = £14580
Therefore, the car will be worth £14580 after 3 years.
(c) The type of correlation between the value of the car and the age of the car is negative correlation. As the age of the car increases, its value decreases. This is because the car depreciates over time, which means its value decreases at a constant rate.