A transport company deposits Rs. 30,000 at the end of every year for 6 years in a sinking fund that earns 10% per annum compounded annually. The amount in the fund just after the 3rd deposit is made is (Given \((1.1)^3 = 1.331\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 99,300
Just after the 3rd deposit, the fund holds 3 deposits made at the end of each year, so its value is the amount of a sinking fund for 3 years; the remaining deposits have not been made yet.
\( \displaystyle A = R\,\frac{(1+i)^n - 1}{i} \)
\( \displaystyle A = 30000 \times \frac{1.331 - 1}{0.1} \)
\( A = 30000 \times 3.31 = 99300 \)
Why the other options are incorrect
Option (1) Rs. 90,000 — Incorrect. This counts the three deposits only and leaves out the interest earned.
Option (2) Rs. 1,19,790 — Incorrect. This lets all of Rs. 90,000 earn interest for 3 years; the deposits were made one by one.
Option (4) Rs. 1,09,230 — Incorrect. This is the amount if the deposits were made at the beginning of each year (99,300 × 1.1).