A sinking fund is created for the redemption of debentures of Rs. 2,00,000 at the end of 25 years. How much money should be provided out of profits each year for the sinking fund, if investment can earn interest 5 % per annum? [Given \( (1.05)^{25}\approx 3.4 \) ]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 4,166.67
The yearly deposits R form an ordinary annuity whose amount (future value) after 25 years must be Rs. 2,00,000:
\( \displaystyle A=R\left[\frac{(1+i)^n-1}{i}\right] \)
\( \displaystyle 200000=R\left[\frac{(1.05)^{25}-1}{0.05}\right] \)
\( \displaystyle =R\left[\frac{3.4-1}{0.05}\right] \)
\( \displaystyle =48R \)
\( \displaystyle R=\frac{200000}{48}\approx 4166.67 \)
So Rs. 4,166.67 must be set aside each year.
CBSE Applied Mathematics (Class XII):
Sinking Fund
