A bond of face value Rs. 8,000 is redeemable at Rs. 105 (per Rs. 100 of face value) at the end of 4 years. If the yield rate is 9% per annum effective, the present value of the amount received on redemption is (Given \((1.09)^{-4} = 0.7084\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 5,950.56
The redemption price is 105% of the face value:
\( C = 1.05 \times 8000 = 8400 \)
Its present value 4 years earlier at 9% effective is
\( C(1+i)^{-n} = 8400 \times (1.09)^{-4} \)
\( = 8400 \times 0.7084 = 5950.56 \)
Why the other options are incorrect
Option (2) Rs. 5,667.20 — Incorrect. This discounts the face value, 8,000 × 0.7084; the bond is redeemed at Rs. 8,400.
Option (3) Rs. 8,400 — Incorrect. This is the redemption amount itself, not its present value.
Option (4) Rs. 5,376 — Incorrect. This takes off simple interest of 36% (4 × 9%) instead of discounting at compound interest.