Rhiannon Corporation has bonds on the market with 18.5 years to maturity, a YTM of 6.50 percent, and a current price of $1,048. The bonds make semiannual payments. What must the coupon rate be on these bonds

6.94%.

Explanation:

The number of coupons payments given is semi annual, the annual will be

= 18.5 years to maturity * 2

= 37 payments.

Annual Yield to Maturity = 6.50 % / 2

= 3.25 %

For coupon payments we use formula:

Bond Price = (Par value / 1 + r^t) + C (1 - 1 / 1 + r^t) / r

$1,048 = ($1,000 / 1.0325^37) + C (1 - 1 / 1.0325^37) / 0.0325

$1,048 = $306.24 + C $21.35

$21.35 * C = $1,048 - $306.24

Coupon Payment C = $741.75 / $21.35

C = $34.74

C = $34.74 * 2 = $69.48

coupon rate = $69.48 / $1,000

Coupon rate = 6.94%.