A trust invests Rs. 5,00,000 at 8% per annum compounded annually. Out of the interest received at the end of every year, Rs. 3,000 is spent on running the trust and the rest is given as a scholarship. If this goes on for ever, the yearly scholarship is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 37,000
A sum P invested at rate i gives a perpetuity of \( R = Pi \) at the end of every year, because only the interest is paid out and the sum itself is never touched.
\( R = 500000 \times 0.08 = 40000 \)
Out of this, Rs. 3,000 goes to running the trust, so the scholarship is
\( 40000 - 3000 = 37000 \)
Why the other options are incorrect
Option (1) Rs. 40,000 — Incorrect. This is the whole yearly interest; the running cost of Rs. 3,000 is also paid out of it.
Option (3) Rs. 43,000 — Incorrect. This adds the running cost to the interest instead of taking it away.
Option (4) Rs. 39,760 — Incorrect. This takes Rs. 3,000 out of the fund itself (8% of 4,97,000); the running cost is paid every year out of the interest.