n January 1, 1987, three 100 par value bonds with 6% annual coupons will mature at the end of 1, 2, and 3 years, respectively. The redemption value of each bond is 100. You are given that the prices for these bonds on January 1, 1987 are: Maturity Date Price December 31, 1987 101.92 December 31, 1988 102.84 December 31, 1989 105.51 These prices are based on an interest rate of i in 1987, j in 1988, and k in 1989. Determine j.

j = 4.52%

Explanation:

face value = $100, with 6% annual coupons

bond₁ matures in 1 year (December 31, 1987), market price $101.92

bond₂ matures in 2 years (December 31, 1988), market price $102.84

bond₃ matures in 3 years (December 31, 1989), market price $105.51

we must determine the market interest rate (j) for bond₂, and to do this we will use the approximate yield to maturity formula:

YTM = {coupon + [(face value - market price)/n]} / [(face value + market price)/2]

YTM = {6 + [(100 - 102.84)/2]} / [(100 + 102.84)/2] = 4.58 / 101.42 = 0.045158 = 4.52%

Since the bonds are sold at a premium, it means that the coupon rate is higher than the market rate.

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