Question

What is the coupon rate of a 8-year, $1000 bond with coupons paid semiannually and a price of $6900, if it has a yield to maturity of 8.5%.?

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Answer #1

Face Value = $1,000
Current Price = $6,900

Annual YTM = 8.50%
Semiannual YTM = 8.50% / 2
Semiannual YTM = 4.25%

Time to Maturity = 8 years
Semiannual Period = 16

Let semiannual coupon be $C

$6,900 = $C * PVIFA(4.25%, 16) + $1,000 * PVIF(4.25%, 16)
$6,900 = $C * (1 - (1/1.0425)^16) / 0.0425 + $1,000 * (1/1.0425)^16
$6,900 = $C * 11.440309 + $513.786847
$C * 11.440309 = $6,386.213153
$C = $558.22

Semiannual Coupon = $558.22

Annual Coupon = 2 * Semiannual Coupon
Annual Coupon = 2 * $558.22
Annual Coupon = $1,116.44

Coupon Rate = Annual Coupon / Face Value
Coupon Rate = $1,116.44 / $1,000
Coupon Rate = 1.1164 or 111.64%

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