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%.?

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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