What price will investors pay for a bond of par value £100, redeemable after 3 years, if the coupon is 8 per cent paid at the end of each year and the market rate of interest in this risk class is 7 per cent?

Question

Quizplus · Accepted Answer

The price of a bond is the present value of its future cash flows, which include the annual coupon payments and the final redemption value. The formula to calculate the price of a bond is:$$ \text{Price} = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) + \frac{F}{(1+r)^n} $$where:- $C$ is the annual coupon payment ($£100 \times 8\% = £8$),- $r$ is the market rate of interest (7% or 0.07),- $n$ is the number of years until maturity (3 years),- $F$ is the face value of the bond (£100).Plugging in the values:$$ \text{Price} = £8 \times \left( \frac{1 - (1 + 0.07)^{-3}}{0.07} \right) + \frac{£100}{(1+0.07)^3} $$$$ \text{Price} = £8 \times 2.6243 + £100 \times 0.8163 $$$$ \text{Price} = £21.00 + £81.63 = £102.63 $$The calculation might slightly vary due to rounding during each step, but the closest answer provided is £102.62, which is option B.

What Price Will Investors Pay for a Bond of Par