Rs. 2,00,000 is invested for one year. How much more interest does it earn at 9% per annum compounded continuously than at 9% per annum compounded annually? (Given \(e^{0.09} = 1.0942\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 840
Under continuous compounding the effective rate is \( e^r - 1 \):
\( e^{0.09} - 1 = 1.0942 - 1 = 0.0942 \)
Interest: \( 200000 \times 0.0942 = 18840 \)
Compounded annually the interest is
\( 200000 \times 0.09 = 18000 \)
The extra interest is
\( 18840 - 18000 = 840 \)
Why the other options are incorrect
Option (1) Rs. 405 — Incorrect. This is the extra interest for half-yearly compounding, 2,00,000 × ((1.045)2 − 1) − 18,000.
Option (2) Rs. 18,840 — Incorrect. This is the whole interest under continuous compounding, not the extra amount.
Option (4) Rs. 1,840 — Incorrect. The interest at 9% compounded annually is Rs. 18,000, so the difference is 18,840 − 18,000 = Rs. 840.