What is the market price of a 5000.00 bond that matures in 9 years and pays 400.00 interest till maturity compounded semi annually?

To calculate the market price of a bond, you need to use the present value formula. This formula takes into account the bond's face value, the interest payments, the interest rate, and the time until maturity.

The market price of a bond can be calculated as the present value of all the future cash flows from the bond. In this case, the cash flows are the periodic interest payments and the final face value payment at maturity.

To calculate the present value of the bond, you'll need to calculate the present value of the interest payments and the present value of the face value payment separately. Then, you add these two present values to get the total market price.

1. Calculate the present value of the interest payments:
The interest payment is $400, and it is paid semi-annually for 9 years, so there will be a total of 18 payments.

You need to calculate the present value of an annuity formula to find the value of these interest payments. The formula to calculate the present value of an annuity is:

PV = PMT * [1 - (1 + r)^(-n)] / r

Where:
PV = Present value of the annuity
PMT = Payment per period ($400 in this case)
r = Interest rate per period (semi-annual rate)
n = Total number of periods (18 in this case)

To calculate the semi-annual interest rate, you need the annual interest rate. Let's assume the annual interest rate is 5%. The semi-annual interest rate would be 5% divided by 2, which is 0.025.

Plug in these values into the formula and solve for PV to get the present value of the interest payments.

2. Calculate the present value of the face value payment:
The face value of the bond is $5000. Since this payment is received at maturity, its present value will be equal to its face value (assuming no discount or premium).

3. Add the present value of the interest payments and the present value of the face value payment to get the total market price of the bond.

Keep in mind that the interest rate used in the calculation should reflect the market rate or the yield to maturity for similar bonds.