Question

A machine costs ₹ 60,000 and its effective life is estimated to be 25 years. A sinking fund is to be created for replacing the machine at the end of its life when its scrap value is estimated as ₹ 5000. The price of the new machine is estimated to be 100% more than the price of the present one. Find the amount that should be set aside at the end of each year, out of the profits, for the sinking fund it accumulates at an interest of 6% per annum compounded annually.

Answer 1

We have A = `"P"/i { (1+i)^n -1}`              ...(i)

Here, A = 60000 + 100% of 60000 - 5000 = 60000 + 60000 - 5000 = 115000

n = 25, `i = (6)/(100)` = 0.06, P = ?

Substituting these values in (i), we obtain

115000 = `"P"/0.06` {(1+0.06)²⁵ -1}

⇒ 0.06 x 115000 = P {(1.06)²⁵ -1}

6900 = P {(1.06)²⁵ -1}                       ...(ii)

Let x = (1.06)²⁵ 

Taking log of both sides, we have

log x = 25 log( 1.06 )
= 25 x 0.0253
= 0.6325
x = Antilog ( 0.6325 ) = 4.29

Now from (ii), 
6900 = P{ 4 .29 -1}

P = `(6900)/(3.29)`
   = Rs. 2097.26
= Rs. 2097 correct to nearest rupee.