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A bond pays a 10.2% coupon on a semi-annual basis. The par value is $1000, and...

A bond pays a 10.2% coupon on a semi-annual basis. The par value is $1000, and the maturity is 15 years. If your required rate is 8%, how much would you be willing to pay for the bond?

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Answer #1

Par Value = $1,000

Annual Coupon Rate = 10.20%
Semiannual Coupon Rate = 5.10%
Semiannual Coupon = 5.10% * $1,000
Semiannual Coupon = $51

Time to Maturity = 15 years
Semiannual Period = 30

Annual YTM = 8.00%
Semiannual YTM = 4.00%

Current Price = $51 * PVIFA(4.00%, 30) + $1,000 * PVIF(4.00%, 30)
Current Price = $51 * (1 - (1/1.04)^30) / 0.04 + $1,000 * (1/1.04)^30
Current Price = $51 * 17.292033 + $1,000 * 0.308319
Current Price = $1,190.21

Therefore, you should pay $1,190.21 for this bond.

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