Question

The zero coupon bond yield curve shows that the one-, two-, and three-year interest rates are...

The zero coupon bond yield curve shows that the one-, two-, and three-year interest rates are 5.0%, 6.3%, and 8.4%, respectively. What is the price of a three-year bond with a face value of $700 and coupons of 12% paid annually

? (a) $703.89 (b) $549.55 (c) $764.48 (d) $698.53 (e) $769.84

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Answer #1

Answer : Option (e ) $ 769.84 is correct option.

Calculation of Price of Three year Bond

Coupon Rate = 12 %

Annual Coupon =700* 12% = $ 84

Discounting to be used in 1 st year (r1) = 5.0% or 0.05

Discounting to be used in 2 st year (r2) = 6.3% or 0.063

Discounting to be used in 3 st year (r3) = 8.4% or 0.084

Current Price = [Coupon / (1+r1)1] + [Coupon / (1+r2)2] +[Coupon / (1+r3)3​​​​​​​] +[Face value / (1+r3)3​​​​​​​]

= [ 84 / (1+0.05)1] + [ 84 / (1+0.063)2] + [ 84 / (1+0.084)3] +[ 700 / (1+0.084)3]

= [ 80 ] + [ 74.338323] + [65.946453] + [549.55377]

= $ 769.838 or $ 769.84

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