Skip to content
Question

Q.A machine costs a company ₹ 52,000 and its effective life is estimated to be 25 years. A sinking fund is created for replacing the machine by a new model at the end of its life time, when its scrap realizes a sum of ₹ 2,500 only. The price of the new model is estimated to be 25% more than the price of the present one. Find what amount should be set aside at the end of each year out of the profits for the sinking fund, if it accumulates at 3⋅5%3\cdot5\% per annum compound. [Given (1⋅035)25=2⋅3632(1\cdot035)^{25} = 2\cdot3632]

CBSECBSE Class XII Board 2025Subjective· 5mImportance★★★★★
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Net replacement amount =65000−2500=62500=65000-2500=62500; from A=R(1+i)n−1iA=R\dfrac{(1+i)^n-1}{i} with i=0.035, n=25i=0.035,\ n=25, R=62500×0.0352.3632−1≈R=\dfrac{62500\times0.035}{2.3632-1}\approx ₹ 1,604.68.

Future value of an ordinary annuity (sinking fund): A=R⋅(1+i)n−1iA=R\cdot\dfrac{(1+i)^{n}-1}{i}, where RR = yearly deposit, ii = annual rate (decimal), nn = number of years, AA = amount to accumulate.

  1. Price of the present machine =₹52000=₹52000; the new model costs 25%25\% more: 52000+0.25×52000=₹6500052000+0.25\times52000=₹65000.
  2. The old machine's scrap at end of life realises ₹2500₹2500, which offsets the cost, so the fund must accumulate the net amount A=65000−2500=₹62500A=65000-2500=₹62500.
  3. Given i=3.5%=0.035i=3.5\%=0.035, n=25n=25 years, and (1.035)25=2.3632(1.035)^{25}=2.3632. …

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.