Question

A machine costs Rs. $98,000$ and its effective life is estimated at $12$ years. If the scrap value is Rs. $3,000$, what should be cut out of the profit at the end of each year to accumulate at compound rate of $5\%$ per annum so that a new machine can be purchased after $12$ years ?

• A. Rs. $6,000$
• B. Rs. $5,968$
• C. Rs. $4,787$
• D. Rs. $4,763$

Answer 1

The correct option is B Rs. $5,968$

Effective cost of the machine is $98000–3000=95000$.

We know that Future value of annuity (FV) $=$ annuity $\times$ Compount Value factor of Annuity (CVAF)

That is $\text{FV}=\text{annuity}\times {\text{CVAF}}_{(5\%,12)}$

$\text{FV}=\text{annuity}\times \left(\frac{(1+r{)}^n-1}{r}\right)$, where $r=0.05,n=12$

$\Rightarrow 95000=\text{annuity}\times \frac{(1+0.05{)}^{12}-1}{0.05}$

$\Rightarrow 95000=\text{annuity}\times \frac{0.795856}{0.05}$

$\Rightarrow 95000=\text{annuity}\times 15.917$

$\therefore \text{annuity}=\frac{95000}{15.917}=5968$

Therefore, Rs. $5,968$ should be cut out of the profit at the end of each year to accumulate at compound rate of $5\%$ per annum, so that a new machine can be purchased after $12$ years.