A three-year bond has 8.0% coupon rate and face value of $1000. If the yield to maturity on the bond is 10%, calculate the price of the bond assuming that the bond makes semi-annual coupon interest payments.

The price of the bond is $943.20.

The formula for calculating the price of a bond is:
Price = (C x (1 - (1 + YTM/2)^-2N)) + (FV x (1 + YTM/2)^-2N)

Where:
C = Coupon rate
YTM = Yield to maturity
N = Number of periods
FV = Face value

In this case, C = 8.0%, YTM = 10%, N = 6 (3 years x 2 semi-annual payments), and FV = $1000.

Plugging these values into the formula, we get:
Price = (8.0% x (1 - (1 + 10%/2)^-12)) + ($1000 x (1 + 10%/2)^-12)
Price = (8.0% x (1 - 0.9756)) + ($1000 x 0.9756)
Price = (8.0% x 0.0244) + ($1000 x 0.9756)
Price = $19.52 + $973.68
Price = $993.20

The price of the bond is $943.20.

To calculate the price of the bond, we need to find the present value of the bond's cash flows, which include both the semi-annual coupon payments and the face value of the bond.

The bond has a coupon rate of 8.0%, which means it pays a coupon of 8.0% * $1000 = $80 per year.
Since the bond makes semi-annual coupon payments, the coupon payment per period is $80 * 0.5 = $40.

The bond has a yield to maturity (YTM) of 10%. Since the bond makes semi-annual payments, we need to adjust the YTM accordingly. The semi-annual yield to maturity is YTM / 2 = 10% / 2 = 5%.

To calculate the present value of the bond's cash flows, we can use the formula for the present value of an annuity:

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

Where:
PV = Present value of the bond
C = Coupon payment per period
r = Semi-annual yield to maturity
n = Number of periods

In this case, C = $40, r = 5%, and n = 3 years * 2 = 6 periods (since there are two periods per year).

Using the formula, we can substitute the values to calculate the price of the bond:

PV = $40 * (1 - (1 + 0.05)^(-6)) / 0.05 + $1000 * (1 + 0.05)^(-6)

Calculating the above equation will give us the price of the bond when semi-annual coupon interest payments are considered.

To calculate the price of the bond, we need to determine the present value of its future cash flows, which include the coupon payments and the face value.

Step 1: Calculate the semi-annual coupon payment.
The coupon rate is 8.0%, and the face value of the bond is $1000. Since the bond makes semi-annual coupon interest payments, the semi-annual coupon payment can be calculated as follows:
Coupon Payment = Coupon Rate × Face Value / 2
Coupon Payment = 8.0% × $1000 / 2
Coupon Payment = $80

Step 2: Determine the number of semi-annual periods until maturity.
Since the bond is a three-year bond with semi-annual coupon payments, the number of semi-annual periods until maturity would be:
Number of Periods = 3 years × 2
Number of Periods = 6 semi-annual periods

Step 3: Determine the discount rate per semi-annual period.
The yield to maturity (YTM) on the bond is 10%. Since the bond makes semi-annual coupon payments, the discount rate per semi-annual period would be half of the YTM. Therefore, the discount rate per semi-annual period is:
Discount Rate = YTM / 2
Discount Rate = 10% / 2
Discount Rate = 5%

Step 4: Calculate the present value of coupon payments.
The present value of the semi-annual coupon payments can be calculated using the formula for the present value of an annuity:
Present Value of Coupon Payments = (Coupon Payment × (1 - (1 + Discount Rate)^-Number of Periods)) / Discount Rate
Present Value of Coupon Payments = ($80 × (1 - (1 + 5%)^-6)) / 5%
Present Value of Coupon Payments = $383.63

Step 5: Calculate the present value of the face value.
The present value of the face value can be calculated directly using the formula for the present value of a single future cash flow:
Present Value of Face Value = Face Value / (1 + Discount Rate)^Number of Periods
Present Value of Face Value = $1000 / (1 + 5%)^6
Present Value of Face Value = $747.26

Step 6: Calculate the price of the bond.
The price of the bond is equal to the sum of the present value of the coupon payments and the present value of the face value:
Bond Price = Present Value of Coupon Payments + Present Value of Face Value
Bond Price = $383.63 + $747.26
Bond Price = $1130.89

Therefore, the price of the bond is $1130.89.