The sales of air-conditioners of a manufacturer is 50000 in 2014. For each air-conditioner sold, the manufacturer gains $500. It is known that the sales increases steadily at a rate of 10% per year, while the gain of each air-conditioner decreases steadily at a rate of 4% per year.
(a) What is the increase in the profit from 2014 to 2015?
(b) Will the profit in 2017 exceed that in 2014 by 20%? Explain your answer.
Let AC denote number of sales of air-conditioners and G/AC gain per air-conditioner sold.
AC: 50 000
Total: 50 000*500 = $25 000 000
To get the numbers for 2015 and 2017 we will use the formula for compound interest
where `C_0` is the starting value (50 000 for the AC) `r` is the rate (10 for the AC and -4 in case of gain because it is decreasing) and `n` is the number of years past (since 2014` ` in this case).
We can get the increase in profit by dividing the total of year 2015 by total of year 2014.
This means that the profit in year 2015 is 105.6% that of the profit in year 2014. In other words profit has increased by 5.6%.
Again, to gain the increase in profit we divide the totals from 2017 and 2014.
Therefore, the increase in profit is 17.76%, meaning that the profit from 2017 will not exceed the profit from 2014 by 20%.