Quarterly changes in population are converted to an annual change by multiplying growth factors. A
growth factor = 1 + i where i is the percentage increase given in decimal form.
The four quarterly increases in the number of staff employed by a particular company last year were
5.6%, 2.1%, – 3% and 1.4%.
To one decimal place, what was the total percentage increase in staff numbers for that year?
To find the total percentage increase in staff numbers for the year, we need to calculate the growth factor for each quarter and then multiply them together.
First, let's convert the percentage increases from decimal form to growth factors:
- The first quarter had an increase of 5.6%, so the growth factor for that quarter is 1 + 0.056 = 1.056.
- The second quarter had an increase of 2.1%, so the growth factor for that quarter is 1 + 0.021 = 1.021.
- The third quarter had a decrease of 3%, so the growth factor for that quarter is 1 - 0.03 = 0.97.
- The fourth quarter had an increase of 1.4%, so the growth factor for that quarter is 1 + 0.014 = 1.014.
To calculate the total growth factor for the year, we multiply the growth factors for each quarter:
1.056 * 1.021 * 0.97 * 1.014 = 1.062201004.
Lastly, to find the total percentage increase in staff numbers, we subtract 1 from the total growth factor and multiply by 100 to convert it to a percentage:
(1.062201004 - 1) * 100 ≈ 6.22.
Therefore, the total percentage increase in staff numbers for that year is approximately 6.2%.