A 30-year 6.000% semi-annual coupon bond has a tenor of 13 years and a yield to maturity of 7.500%. In percent of PAR, what is the price of the bond today?

Expert Solution

Par Value of Bond = $1,000

Annual Coupon Rate = 6.000%
Semiannual Coupon Rate = 3.000%
Semiannual Coupon = 3.000% * $1,000
Semiannual Coupon = $30

Time to Maturity = 13 years
Semiannual Period = 26

Annual YTM = 7.500%
Semiannual YTM = 3.75%

Current Price of Bond = $30 * PVIFA(3.75%, 26) + $1,000 * PVIF(3.75%, 26)
Current Price of Bond = $30 * (1 - (1/1.0375)^26) / 0.0375 + $1,000 * (1/1.0375)^26
Current Price of Bond = $30 * 16.427185 + $1,000 * 0.383981
Current Price of Bond = $876.80

Price in Percent of Par Value = Current Price of Bond / Par Value of Bond
Price in Percent of Par Value = $876.80 / $1,000
Price in Percent of Par Value = 87.68%

jeff jeffy answered 2 years ago

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