A firm intends to create a sinking fund to replace at the end of 20th year assets costing Rs. 10,00,000. If the interest rate is 5 % per annum, then the amount to be retained out of profits at the end of every year is:
[ Given that : \( (1.05)^{20}=2.6532 \)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 30244.37
For a sinking fund with yearly payment \( A \), amount \( S \), rate \( i \) and \( n \) years,
\( \displaystyle A=\frac{S\,i}{(1+i)^{n}-1} \)
Substituting \( S=10{,}00{,}000 \), \( i=0.05 \) and \( (1.05)^{20}=2.6532 \):
\( \displaystyle A=\frac{50{,}000}{2.6532-1} \)
\( \displaystyle =\frac{50{,}000}{1.6532} \)
\( \displaystyle \approx 30{,}244.37 \)
So Rs. 30244.37 is retained every year.
CBSE Applied Mathematics (Class XII):
Sinking Fund
