A society deposits Rs. 15,000 at the end of every six months in a sinking fund for 3 years. If the fund earns 10% per annum compounded half-yearly, the total interest earned by the fund in the 3 years is (Given \((1.05)^6 = 1.3401\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 12,030
The interest earned is the amount in the fund minus the total of the deposits.
For half-yearly deposits,
\( \displaystyle R = 15000,\quad i = \frac{0.10}{2} = 0.05,\quad n = 6 \)
The amount in the fund is
\( \displaystyle A = 15000 \times \frac{1.3401 - 1}{0.05} \)
\( A = 15000 \times 6.802 = 102030 \)
The total of the deposits is
\( 15000 \times 6 = 90000 \)
So the interest earned is
\( 102030 - 90000 = 12030 \)
Why the other options are incorrect
Option (1) Rs. 1,02,030 — Incorrect. This is the whole amount in the fund; the deposits of Rs. 90,000 must be taken away.
Option (2) Rs. 9,000 — Incorrect. This is just 10% of the deposits; each deposit earns interest for a different length of time.
Option (4) Rs. 17,131.50 — Incorrect. This is 1,02,030 × 1.05 − 90,000, the interest when the deposits are made at the beginning of each half-year.