Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?

Correct result:

p =  11.3987 %

Solution:

$$\begin{gathered} q=(1+{\displaystyle \frac{25}{100}})\cdot (1+{\displaystyle \frac{40}{100}})\cdot (1-{\displaystyle \frac{20}{100}})\cdot (1+{\displaystyle \frac{10}{100}})={\displaystyle \frac{77}{50}}=1{\displaystyle \frac{27}{50}}=1.54 \\ {p}_1=100\cdot (q-1)=100\cdot (1.54-1)=54\mathrm{\%} \\ {q}_2=q^{1\mathrm{/}4}=\sqrt[4]{1.54}\doteq 1.114 \\ p=100\cdot (q_2-1)=100\cdot (1.114-1)\mathrm{\%}=11.3987\mathrm{\%} \end{gathered}$$

Try another example

Showing 1 comment:

Math student

One example about progression in percentage and depressed in percentage

4 months ago  Like

Related math problems and questions:

• Annual growth
  The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%?
• Volume of wood
  Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
• 3y inflation
  Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
• Standard deviation
  Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
• Investment
  1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
• Radioactive material
  A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
• Inflation
  Once upon a time, tsar owned a money printer and printed and printed. The result of printing money prices went up,in the first year 3.9 %, in the second 6%, in the third 4.7% and in the fourth 5.5%. Then tsar was failed in election. Calculate the average
• Population
  The town has 65,000 inhabitants. 40 years ago, there were 157,000. How many people will live in a city in 10 years if the population's average rate is as in previous years?
• Percent change
  If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
• Sale
  If the product twice price cut by 25%, what percentage was price cut in total?
• The town
  The town population is 56000. It is decreasing by 2% every year. What will be the population of the town after 13 years?
• Population
  What is the population of the city with 3% annual growth, if in 10 years the city will have 60,000 residents?
• The city
  At the end of 2010 the city had 248000 residents. The population increased by 2.5% each year. What is the population at the end of 2013?
• The notebook
  After rising by 40%, the notebook cost 10.50 euros. How much did this notebook cost if it increased in price by only 20% instead of 40%?
• Geometric sequence
  In the geometric sequence is a₄ = 20 a₉ = -160. Calculate the first member a₁ and quotient q.
• Salary in enterprise
  The average salary in the company is 27 000 CZK, 30% of workers have the lowest average income of 19 thousand CZK. There were an increase in the salary in this group by 2%. How much % increased the average salary across the company?
• The raw
  The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35