Mathematics for FinanceMTP Dec 23 - Series IIQuestion 1592 of 512
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A 1000\displaystyle 1000 bond paying annual dividends at 8.5%\displaystyle 8.5\% will be redeemed at par at the end of 10\displaystyle 10 years. Find the purchase price of this bond if the investor wishes a yield rate of 8%\displaystyle 8\%.

Options

A907.135\displaystyle 907.135
B1033.54\displaystyle 1033.54
C945.67\displaystyle 945.67
DNone of these
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Correct Answer

✅ Option b — 1033.54\displaystyle 1033.54

All Options:

  • A907.135\displaystyle 907.135
  • B1033.54\displaystyle 1033.54
  • C945.67\displaystyle 945.67
  • DNone of these

Detailed Solution & Explanation

The purchase price of the bond is: P=C×P(n,r)+FV(1+r)nP = C \times P(n, r) + \frac{FV}{(1+r)^n} Given: * Par Value (FV\displaystyle FV) = 1,000\displaystyle 1,000 * Dividend (coupon rate) = 8.5%\displaystyle 8.5\% p.a., so annual coupon C=1,000×8.5%=85\displaystyle C = 1,000 \times 8.5\% = 85 * Time (n\displaystyle n) = 10\displaystyle 10 years * Yield rate (r\displaystyle r) = 8%\displaystyle 8\% p.a. = 0.08\displaystyle 0.08 The present value is: P=85×[1−(1.08)−100.08]+1,000(1.08)10P = 85 \times \left[ \frac{1 - (1.08)^{-10}}{0.08} \right] + \frac{1,000}{(1.08)^{10}} Using (1.08)−10≈0.463193\displaystyle (1.08)^{-10} \approx 0.463193: P=85×6.71008+1,000×0.463193≈570.36+463.19=1,033.55P = 85 \times 6.71008 + 1,000 \times 0.463193 \approx 570.36 + 463.19 = 1,033.55 Hence, **Option B** is the correct answer.

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