A corporation has bonds on the market with 13.5 years to maturity, a YTM of 7.6 percent, and a current price of $1,175. The bonds make semiannual payments. What must the coupon rate be on these bonds?

To calculate the coupon rate on these bonds, we can use the formula for the present value of a bond:

PV = (C / (1 + r/2)^n) + (F / (1 + r/2)^n)

Where:
PV = Present value of the bond = $1,175
C = Coupon payment
r = Yield to maturity (YTM) as a decimal = 7.6% / 100 = 0.076
n = Number of coupon payment periods = 13.5 * 2 = 27 (since the bonds make semiannual payments)
F = Face value of the bond

We are given that the bonds have 13.5 years to maturity, which means there are a total of 13.5 * 2 = 27 coupon payments.

Since the bonds are currently priced at $1,175, we can substitute these values into the formula and solve for C.

$1,175 = (C / (1 + 0.076/2)^27) + (F / (1 + 0.076/2)^27)

Let's assume the face value of the bond is $1,000 (this is a common assumption for many bonds).

$1,175 = (C / (1.038)^27) + ($1,000 / (1.038)^27)

Now we can solve this equation to find the coupon payment (C).

$1,175 - $1,000 = C / (1.038)^27

$175 = C / (1.038)^27

$175 = C / 1.970447

C = $175 * 1.970447

C ≈ $345.31

Therefore, the coupon rate on these bonds must be approximately $345.31.

To find the coupon rate on the bonds, we need to use the formula for the bond price and solve for the coupon rate. The formula for the price of a bond can be written as:

Bond Price = (C × (1 - (1 + r)^(-n))) / r + (F / (1 + r)^n)

Where:
C = Coupon payment
r = Yield to Maturity (YTM) / 2
n = Number of periods

In this case, we are given the following information:
YTM = 7.6% = 0.076
Bond Price = $1,175
n = 13.5 years (since payments are semiannual, n is multiplied by 2)

Now we can substitute these values into the formula:

$1,175 = (C × (1 - (1 + 0.076/2)^(-(13.5*2)))) / (0.076/2) + (F / (1 + 0.076/2)^(13.5*2))

We want to solve for C (the coupon payment). We need the value of F (the face value) to solve the equation. However, it is not provided in the information given. Hence, we cannot calculate the exact coupon rate without the face value of the bond.

If you have the face value information for the bond, you can substitute it into the equation and solve for C to find the coupon rate.