To determine whether the bond is selling at a premium, discount, or at par, we need to calculate the present value of the bond's future cash flows, given the current yield to maturity.

Here are the steps:

1. Calculate the present value of the bond's future coupon payments. The bond pays $23 every six months for the remaining life of the bond, which is 7 years (since the bond was issued 3 years ago and it's a 10-year bond). That's a total of 14 payments. The yield to maturity is 4.8% per annum, compounded semi-annually, so the discount rate per period is 4.8%/2 = 2.4%.

The present value of an annuity formula is: PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $23 * [(1 - (1 + 0.024)^-14) / 0.024] = $23 * 11.982 = $275.586

2. Calculate the present value of the bond's face value. The face value is the amount the bondholder will receive at the end of the bond's life, which is $1000. We discount this back to the present using the formula: PV = FV / (1 + r)^n, where FV is the face value, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $1000 / (1 + 0.024)^14 = $1000 / 1.389 = $719.914

3. Add the present values of the coupon payments and the face value to get the bond's current price: $275.586 + $719.914 = $995.5

Since the bond's current price ($995.5) is less than its face value ($1000), the bond is selling at a discount. So, the answer is "discount".

Question

To determine whether the bond is selling at a premium, discount, or at par, we need to calculate the present value of the bond's future cash flows, given the current yield to maturity.

Here are the steps:

1. Calculate the present value of the bond's future coupon payments. The bond pays $23 every six months for the remaining life of the bond, which is 7 years (since the bond was issued 3 years ago and it's a 10-year bond). That's a total of 14 payments. The yield to maturity is 4.8% per annum, compounded semi-annually, so the discount rate per period is 4.8%/2 = 2.4%.

The present value of an annuity formula is: PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $23 * [(1 - (1 + 0.024)^-14) / 0.024] = $23 * 11.982 = $275.586

2. Calculate the present value of the bond's face value. The face value is the amount the bondholder will receive at the end of the bond's life, which is $1000. We discount this back to the present using the formula: PV = FV / (1 + r)^n, where FV is the face value, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $1000 / (1 + 0.024)^14 = $1000 / 1.389 = $719.914

3. Add the present values of the coupon payments and the face value to get the bond's current price: $275.586 + $719.914 = $995.5

Since the bond's current price ($995.5) is less than its face value ($1000), the bond is selling at a discount. So, the answer is "discount".

Knowee AI · Accepted Answer

To determine whether the bond is selling at a premium, discount, or at par, we need to calculate the present value of the bond's future cash flows, given the current yield to maturity.

Here are the steps:

1. Calculate the present value of the bond's future coupon payments. The bond pays $23 every six months for the remaining life of the bond, which is 7 years (since the bond was issued 3 years ago and it's a 10-year bond). That's a total of 14 payments. The yield to maturity is 4.8% per annum, compounded semi-annually, so the discount rate per period is 4.8%/2 = 2.4%.

The present value of an annuity formula is: PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $23 * [(1 - (1 + 0.024)^-14) / 0.024] = $23 * 11.982 = $275.586

2. Calculate the present value of the bond's face value. The face value is the amount the bondholder will receive at the end of the bond's life, which is $1000. We discount this back to the present using the formula: PV = FV / (1 + r)^n, where FV is the face value, r is the discount rate per period, and n is the number of periods.

Substituting the given values, we get: PV = $1000 / (1 + 0.024)^14 = $1000 / 1.389 = $719.914

3. Add the present values of the coupon payments and the face value to get the bond's current price: $275.586 + $719.914 = $995.5

Since the bond's current price ($995.5) is less than its face value ($1000), the bond is selling at a discount. So, the answer is "discount".

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