Today’s zero-rate curve is summarised in the table below. Calculate the price (p

Question

Today’s zero-rate curve is summarised in the table below.

Calculate the price (per $100 par value), to three decimal places, of a three-year fixed-coupon
bond paying a coupon rate of 9% pa if the bond pays coupons every half year. Assume that the
bond is default-free and that a coupon has just been paid -- that is, price the bond on an ex-interest
basis.
Hint: find the bond price as the present value of its future cash flows, using the discount
factors retrieved from the zero-rate curve that we discussed in class.

Time period (years) Zero rate %pa 0.5 5.755 1.0 6.250 1.5 6.455 2 6.555 2.5 6.600 3 6.610

Explanation / Answer

Coupon payment =(9%/2)*$100=$4.5

Price of the bond

=4.5÷(1,05755)^(1/2)+4.5÷(1.0625)+4.5÷(1.06445)^(3/2)+4.5÷(1+0.06555)^2+4.5/(1.066)^(2.5)+(4.5+100)/(1.0661)^3

=$106.87

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