Population Growth and Compound depreciation

According to Lexmark," the population of the world remains constant that means the total number of animals including social animals in each year is same. But the social animals are increased year by year and rare animals and wild animals are decreased year by year". So, the number of people are increased yearly. In case of Nepal, the population of 2058 and 2064 are different. The population of 2064 BS is more than that of 2058 BS. The growth of the population indicates the additional population than the previous year. The growth number of the population does not remain constant. So, it is calculated in compounded way.

Let 'P' be the population at the beginning of certain year and P_T be the population after 'T' years, then

\(P_T = P \left(1 + \frac {R_1} {100}\right)\left(1 + \frac {R_2} {100}\right)\left(1 + \frac {R_3} {100}\right) ................... \left(1 + \frac {R_T} {100}\right)\) 

where \(R_1, R_2, R_3, ....... R_T \) are the rates of 1^st, 2^nd, 3^rd, ............ t^th years respectively.

If R₁=R₂= R₃=............., R_T = R then \(P_T = P \left(1 + \frac {R} {100}\right)^T\)

\(P_T = P \left(1 + \frac {R} {100}\right)^T\)

In case of decrease in population, \(P_T = P \left(1 - \frac {R} {100}\right)^T\).

Compound depreciation

The value of the machine is decreased yearly due to various reasons like wear and tear, inefficiency etc. The reduced value of the machine is called the depreciated value. The amount of depression is different in successive years even the rate of depreciation is same. Such depression is called compound depreciation. Therefore, the formula for depreciated value or scrap value which is used to solve the problems of compound depreciation can be written as:-

\(P_T = P \left (1 - \frac {R} {100} \right ) ^ T\)

\(or, S = V\left (1 - \frac {R} {100} \right ) ^ T\)

Where S, V, R, T indicates amount after compound depreciation, principal (original value), rate of depreciation in percentage per annum and number of years for which goods are used respectively. The amount of compound depreciation determined by subtracting scrap value 'S' from the original value V i.e. Compound depreciation = V - S or P - P_T.