As compared to its first year of operation, ABC Company grew 8% in the second year and an additional 2% per year for the next two years. If total growth for years 2-4 was $45,000 over the first year’s sales of $150,000, how much did ABC Company grow in year 2?
Discard the noise about years 3 and 4.
ABC grew 8% of 150,000 = 12000
As you can see, the numbers don't add up even close:
150000(1.08*1.02^2 - 1) = 18,544.80
Where did the 45,000 come from?
To find out how much ABC Company grew in year 2, we first need to calculate the growth in year 2 as a percentage of the first year's sales.
Let's represent the growth in year 2 as x:
Growth in year 2 = x% of the first year's sales
According to the problem, the total growth for years 2-4 was $45,000. So, the total growth over the first year's sales can be written as:
Total growth = Growth in year 2 + Growth in year 3 + Growth in year 4
$45,000 = Growth in year 2 + 2% of the first year's sales + 2% of the first year's sales
Since the growth in year 2 is x% of the first year's sales, we can write it as:
Growth in year 2 = x% of the first year's sales = x/100 * $150,000
The growth in year 3 and year 4 is an additional 2% per year. So, we can write it as:
Growth in year 3 = 2% of the first year's sales = 2/100 * $150,000
Growth in year 4 = 2% of the first year's sales = 2/100 * $150,000
Now, let's substitute these values into the equation for total growth:
$45,000 = x/100 * $150,000 + 2/100 * $150,000 + 2/100 * $150,000
Simplifying the equation, we get:
$45,000 = x/100 * $150,000 + (2 + 2)/100 * $150,000
$45,000 = x/100 * $150,000 + 4/100 * $150,000
Combining like terms, we have:
$45,000 = (x + 4)/100 * $150,000
To solve for x, we can multiply both sides of the equation by 100 and divide by $150,000:
$45,000 * $150,000 = (x + 4) * 100
6,750,000 = 100x + 400
Simplifying further:
6,750,000 - 400 = 100x
6,749,600 = 100x
Dividing by 100:
x = 6,749,600 / 100
x = 67,496
Therefore, ABC Company grew by $67,496 in year 2.