Answer:To find the coupon rate of the bonds, we need to use the formula for calculating the present value of a bond:
PV = C * [1 - (1 + r)^(-n)] / r + F * (1 + r)^(-n)
Where PV is the present value of the bond, C is the coupon payment, r is the yield to maturity (YTM), n is the number of periods until maturity, and F is the face value of the bond.
In this case, we are given the following information:
- YTM (r) = 7.6% = 0.076
- Number of periods until maturity (n) = 13 years, so there are 13 * 2 = 26 semiannual periods.
- Face value (F) = $1,000
- Current price (PV) = $901.98
We can substitute these values into the formula and solve for C, the coupon payment:
$901.98 = C * [1 - (1 + 0.076)^(-26)] / 0.076 + $1,000 * (1 + 0.076)^(-26)
Simplifying the equation, we can solve for C:
$901.98 = C * [1 - (1.076)^(-26)] / 0.076 + $1,000 * (1.076)^(-26)
Solving this equation, we find that C ≈ $60.67.
To find the coupon rate, we can divide the coupon payment (C) by the face value (F) and multiply by 100 to express it as a percentage:
Coupon rate = (C / F) * 100 ≈ ($60.67 / $1,000) * 100 ≈ 6.07%
Therefore, the coupon rate of the bonds is approximately 6.07%.
Step-by-step explanation: