Question

(a) The annual rates of growth of output of a factory in five years are 5.0,7.5,2.5,5.0 and 10.0 percent respectively. What is the compound rate of growth
of output per annum for the period ?​

Answer 1

Step-by-step explanation:

Given  

(a) The annual rates of growth of output of a factory in five years are 5.0,7.5,2.5,5.0 and 10.0 percent respectively.  What is the compound rate of growth  of output per annum for the period ?​

Year        growth rate   Production taking 100 in the beginning       log x

  1                   10%                                                 105                       2.0212                          

  2                     7.5%                                              107.5                   2.0314                            

  3                     2.5%                                              102.5                   2.0107                              

  4                        5%                                              105                      2.0212                              

  5                       10%                                             110                       2.0414                            

                                                                                     So  ∑ log x = 10.1259

                           Therefore G.M = antilog (∑ log x / n)

                                                    = antilog (10.1259 / 5)

                                                    = antilog (2.02518)

                                                   = 105.9

Therefore average rate of growth = 105.9 – 100

                                                      = 5.9%

Answer 2

The compound rate of growth per annum would be 14.87% .

Step-by-step explanation:

The formula to calculate the compound annual rate of growth (CAGR) :

$\text{Compound rate of growth}=(\frac{V_n}{V_0})^{\frac{1}{n}}-1$

$V_{n}$ = ending value

$V_{0}$ = The beginning value

n = number of periods

$=(\frac{10}{5})^{\frac{1}{5}}-1$

= 1.14869835 - 1

= 0.14869835

= 14.87% per year

The compound rate of growth per annum would be 14.87% .

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