A company has issued debentures of Rs. 10,00,000 that must be repaid at the end of 8 years. To repay them, it sets aside an equal amount at the end of every year in a sinking fund that earns 5% per annum compounded annually. The yearly amount is (Given \((1.05)^8 = 1.4775\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 1,04,712.04
For a sinking fund that must reach A in n years at rate i, the deposit R at the end of each year satisfies
\( \displaystyle A = R\,\frac{(1+i)^n - 1}{i} \)
Here A = 10,00,000, i = 0.05 and n = 8:
\( \displaystyle 1000000 = R \times \frac{1.4775 - 1}{0.05} \)
\( 1000000 = R \times 9.55 \)
\( \displaystyle R = \frac{1000000}{9.55} = 104712.04 \)
Why the other options are incorrect
Option (1) Rs. 1,25,000 — Incorrect. This is 10,00,000 ÷ 8, which ignores the interest the fund earns.
Option (2) Rs. 99,725.75 — Incorrect. This is 1,04,712.04 ÷ 1.05, the deposit if it were made at the beginning of each year.
Option (3) Rs. 1,54,712.04 — Incorrect. This treats Rs. 10,00,000 as a loan taken today and finds its yearly instalment; the sinking fund has to build the sum up by the end of 8 years.