Question

A machine costing Rs $2$ lacs has effective life of $7$ years and its scrap value is Rs $30000$. What amount (in Rs) should the company put into a sinking fund earning $5\%$ per annum so that it can replace the machine after its useful life? Assume that a new machine will cost Rs $3$ lacs after $7$ years.

• A. $30161.35$
• B. $33101.35$
• C. $33161.35$
• D. $33111.35$

Answer 1

The correct option is C $33161.35$

$\Rightarrow$ Cost of new machine is $Rs.3lacs$

$\Rightarrow$ Scrap value of old machine is $Rs.30000$

$\Rightarrow$ Hence, money required for new machine after 7 years = $Rs.300000-Rs.30000=Rs.270000$.

$\Rightarrow$ If A is the annual deposit into sinking fund, then we have

$\Rightarrow$ Amount of annuity, $M=Rs.270000$

$\Rightarrow$ Number of periods = $7years$

$\Rightarrow$ $r=5\%=0.05$

$\therefore$ $M=\frac{A}{r}\times \left[\right(1+r{)}^n-1]$

$\Rightarrow$ $270000=\frac{A}{0.05}\times \left[\right(1.05{)}^7-1]$

$\Rightarrow$ $A=\frac{270000\times 0.05}{(1.05{)}^7-1}$

$\therefore$ $A=33161.35$ Rs