A company sets aside Rs. M at the end of each year to be able to buy a machine expected to cost Rs. 20 lakh at the end of 8 years and the rate of interest is 10 % per annum. The correct calculation of M is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{0.1\times 20{,}00{,}000}{(1.1)^8-1} \)
The yearly payments form a sinking fund, an ordinary annuity whose amount after n years must equal the cost of the machine:
\( \displaystyle S=M\left[\frac{(1+i)^n-1}{i}\right] \)
\( \displaystyle M=\frac{S\times i}{(1+i)^n-1} \)
Here S = Rs. 20 lakh = Rs. 20,00,000, i = 0.1 and n = 8:
\( \displaystyle M=\frac{0.1\times 20{,}00{,}000}{(1.1)^8-1} \)
Why the other options are incorrect
Option (1) \( \displaystyle\frac{0.1\times 2{,}00{,}000}{(1.1)^9-1} \) — Incorrect. This uses Rs. 2,00,000 (2 lakh) instead of Rs. 20,00,000 (20 lakh), and the power 9 instead of 8.
Option (2) \( \displaystyle\frac{0.1\times 20{,}00{,}000}{(1.1)^7-1} \) — Incorrect. The fund runs for 8 years, so the power is 8, not 7.
Option (4) \( 0.1\times 20{,}00{,}000\times(1.1)^8 \) — Incorrect. The amount of the annuity is divided by \( (1.1)^8-1 \), not multiplied by \( (1.1)^8 \).
CBSE Applied Mathematics (Class XII):
Sinking Fund
