Question

A $1,000 par value bond is currently valued at $1,055. The bond pays interest semi-annually, has 10 years to maturity, and has a yield to maturity of 7.3 percent. The coupon rate is _____ percent and the current yield is _____ percent.

Answer #1

Par Value = $1,000

Current Value = $1,055

Time to Maturity = 10 years

Semiannual Period = 20

Annual YTM = 7.30%

Semiannual YTM = 3.65%

Let Semiannual Coupon be $C

$1,055 = $C * PVIFA(3.65%, 20) + $1,000 * PVIF(3.65%, 20)

$1,055 = $C * (1 - (1/1.0365)^20) / 0.0365 + $1,000 /
1.0365^20

$1,055 = $C * 14.021422 + $488.218095

$566.781905 = $C * 14.021422

$C = $40.42

Semiannual Coupon = $40.42

Annual Coupon = 2 * Semiannual Coupon

Annual Coupon = 2 * $40.42

Annual Coupon = $80.84

Coupon Rate = Annual Coupon / Par Value

Coupon Rate = $80.84 / $1,000

Coupon Rate = 0.0808 or 8.08%

Current Yield = Annual Coupon / Current Price

Current Yield = $80.84 / $1,055

Current Yield = 0.0766 or 7.66%

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