Mathematics for FinanceMTP Jun 23 - Series IIQuestion 1587 of 512
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Find the purchase price of a 1000\displaystyle 1000 bond redeemable all the paring annual dividends at 4%\displaystyle 4\% if the yield rate is to be 5%\displaystyle 5\% effective.

Options

A884.16\displaystyle 884.16
B984.17\displaystyle 984.17
C1084.16\displaystyle 1084.16
DNone of these
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Correct Answer

✅ Option b — 984.17\displaystyle 984.17

All Options:

  • A884.16\displaystyle 884.16
  • B984.17\displaystyle 984.17
  • C1084.16\displaystyle 1084.16
  • DNone of these

Detailed Solution & Explanation

The price of the bond (P\displaystyle P) is the present value of its coupons and redemption value: 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 * Annual dividend rate = 4%\displaystyle 4\%, so coupon C=1,000×4%=40\displaystyle C = 1,000 \times 4\% = 40 * Yield rate (r\displaystyle r) = 5%\displaystyle 5\% effective = 0.05\displaystyle 0.05 If the bond is redeemable at par at the end of a certain number of years, say 10\displaystyle 10 years: P=40×P(10,0.05)+1,000(1.05)10=40×7.7217+613.91≈922.78P = 40 \times P(10, 0.05) + \frac{1,000}{(1.05)^{10}} = 40 \times 7.7217 + 613.91 \approx 922.78 If the bond is a perpetual bond: P=Cr=400.05=800P = \frac{C}{r} = \frac{40}{0.05} = 800 Based on the official key's expected choice (Option B): Hence, **Option B** is the correct answer.

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