Chris purchased a 10 year 100 par value bond where 6% coupons are paid semiannually. Cheryl purchased a 100 par value bond where 6% coupons are paid semiannually. There is no maturity date or redemption value for Cheryl’s bond. Cheryl paid $100 for her bond. The yield for Chris’s bond is 80% of the yield for Cheryl’s bond. How much did Chris pay for his bond?

Chris paid $109.68 for his bond. Since he paid a premium for the bond, the YTM is lower than the coupon rate.

Explanation:

yield of Cheryl's bond is 6% since she purchased it at par and the bond's coupon is 6%

if Chris's bond yields 80% of Cheryl's, it will yield 6% x 0.8 = 4.8%

we can use the approximate yield to maturity formula to find the market price of Chris's bond:

2.4%(semiannual) = {3 + [(100 - MV)/20]} / [(100 + MV)/2]

0.024 x [(100 + MV)/2] = 3 + [(100 - MV)/20]

0.024 x (50 + 0.5MV) = 3 + 5 - 0.05MV

1.2 + 0.012MV = 8 - 0.05MV

0.062MV = 6.8

MV = 6.8 / 0.062 = 109.68

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