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 grow in year 2?
To find out how much ABC company grew in year 2, we need to calculate the growth rate for each of the four years and then add them together.
Let's start by finding the growth rate for each year:
Year 2 growth rate: 8%
Year 3 growth rate: 2%
Year 4 growth rate: 2%
Now, let's calculate the growth in sales for each year:
Year 2 growth = 8% of Year 1 sales = 0.08 * $150,000 = $12,000
To find out the growth in sales for years 3 and 4, we need to use the compound interest formula. The growth in sales for each of these two years would be 2% of the previous year's sales, plus the growth in sales from the previous year.
Year 3 growth = (2% of Year 2 sales) + Year 2 growth
= (0.02 * Year 2 sales) + Year 2 growth
= (0.02 * $150,000) + $12,000
Year 4 growth = (2% of Year 3 sales) + Year 3 growth
= (0.02 * Year 3 sales) + Year 3 growth
= (0.02 * (0.02 * $150,000 + $12,000)) + (0.02 * $150,000 + $12,000)
Now, let's add up the growth in sales for years 2, 3, and 4:
Total growth = Year 2 growth + Year 3 growth + Year 4 growth
= $12,000 + [(0.02 * $150,000) + $12,000] + [(0.02 * (0.02 * $150,000 + $12,000)) + (0.02 * $150,000 + $12,000)]
Finally, we know that the total growth for years 2-4 was $45,000, so we can set up the following equation:
$45,000 = Total growth
Now, you can solve the equation to find the value of Year 2 growth, which is the original question.