Problema Solution
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?
Answer provided by our tutors
The problem statement contains errors, so we make the following assumptions:
1. We assume that "how much did ABC Company grow in year 2?" should really be stated as "how much did ABC Company grow in year 4?"
2. we assume 8% in the second year is really 8% in the first year, taking the first year's sales of $150,000 to be "year zero"
without these assumptions the question is unintelligible
The initial sales were $150,000
8% growth after the first year, gives total sales of:
150000 + 150000*0.08 = 162000
2% growth in years 2 and 3 gives total sales of:
162000 + 162000 * 0.02 = 165240
165240 + 165240 * 0.02 = 168544.8
the total growth, in dollars, over years 1-3 can be said to be:
150000*0.08 + 162000 * 0.02 + 165240 * 0.02 = 18544.8
of the total growth over years 2-4 was $45000, then the year 4 growth was:
45000 - 18544.8 = 26455.2
so we calculate what percentage, 'x', 26455.2 is of the sales at end of year 3, 18544.8:
18544.8 + 185448.8*x = 18544.8 + 26455.2
185448.8*x = 26455.2
x = 26455.2/185448.8 = 0.14265
ABC Company grew approximately 14.3% in the year we are interpreting to be year 4