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?
growth factor in first year = 1+r
growth factor in 2nd year = 1.08
growth factor in 3rd and 4th year = 1.02
so 150000(1+r)(1.08)(1.02)^2 = 150000+45000
1+r = 195000/(150000(1.08)(1.02)^2)
1+r = 1.15696
r = .15696 = 15.696fi
or appr 15.7 %
so at end of first year sales were
150000(1.15696) = 17354.44
at the end of 2nd year sales were
17354.44(1.08) = 18742.79
growth in 2nd year would be that difference
= $1,388.35
that should be $13,883.52 in the last line as the answer
circle the word that completes each sentence
To find out how much ABC Company grew in year 2, we first need to calculate the growth rate of each year.
Let's break it down:
Year 1: Sales = $150,000 (baseline)
Year 2: Growth = 8% (compared to year 1's sales)
Sales = $150,000 + (8% of $150,000)
Year 3 onwards: Growth per year = 2% (compared to the previous year's sales)
Sales in Year 3 = sales in Year 2 + (2% of sales in Year 2)
Sales in Year 4 = sales in Year 3 + (2% of sales in Year 3)
Given that the total growth for years 2-4 was $45,000 over the first year's sales, we can write the equation:
Sales in Year 2 + Sales in Year 3 + Sales in Year 4 - $150,000 = $45,000
Now, let's calculate each year's sales:
Sales in Year 2 = $150,000 + (8% of $150,000) = $150,000 + ($0.08 * $150,000) = $150,000 + $12,000 = $162,000
Sales in Year 3 = $162,000 + (2% of $162,000) = $162,000 + ($0.02 * $162,000) = $162,000 + $3,240 = $165,240
Sales in Year 4 = $165,240 + (2% of $165,240) = $165,240 + ($0.02 * $165,240) = $165,240 + $3,304.8 = $168,544.8
Now let's substitute these values back into the equation:
$162,000 + $165,240 + $168,544.8 - $150,000 = $45,000
Simplifying the equation, we have:
$345,784.8 - $150,000 = $45,000
$195,784.8 = $45,000
So, ABC Company grew $45,000 in year 2.