185k views
4 votes
Compute the Market Value of a Bond Today

The Bond Face Value of $1,000,
The Bond Maturity Date is 10 years from Now.
The Face Contract Interest Rate is 8% paid annually.
The Market Rate of Interest is 6%.
Round your Answer to the nearest dollar, no commas, dollar signs or decimals, enter as a Number only.
Use the PV+FV Tables from the Website.

1 Answer

6 votes

Final answer:

To calculate the market value of a bond, you need to discount its future cash flows, which include annual interest payments and the principal at maturity, to their present value using the market interest rate.

Step-by-step explanation:

The market value of a bond represents the present value of its future cash flows, which consist of periodic interest payments and the lump sum principal repayment at maturity. To compute the market value of a bond with a face value of $1,000, an 8% contract interest rate paid annually, and a 10-year maturity when the market rate of interest is 6%, we use the formula for present value.

First, we calculate the annual interest payment, which is the face value multiplied by the contract interest rate: $1,000 x 8% = $80.

Using the present value of an annuity formula, we discount these annual payments at the market interest rate of 6%. Then we add the present value of the face value, also discounted at the market rate for 10 years.

The present value of annuity formula is: PV = PMT x [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the market discount rate, and n is the number of periods. The simplified formula for the present value of a single sum in the future is: PV = FV / (1 + r)^n, where FV is the face value.

Applying these formulas, we'd arrive at the present value of the bond's annual interest payments and the principal repayment at maturity. Remember, to find the total market value of the bond, we sum these two present values. Round the final answer to the nearest dollar.

User Roger Leblanc
by
7.9k points