Question

A bond with a face value of $22,000 and a 5.6% interest rate (compounded semiannually) will mature in 11 years. What is a fair price to pay for the bond today? A fair price to buy the bond at would be $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

A fair price to pay for the bond today would be $14,735.95.

Step by Step Explaination:

To calculate the fair price of the bond, we can use the present value formula for a bond:

`\[PV = (F)/((1 + (r)/(n))^(nt))\]`

Where:

-
`\(PV\)` is the present value or fair price of the bond,

-
`\(F\)` is the face value of the bond,

- r is the annual interest rate (as a decimal),

- n is the number of times interest is compounded per year,

- t is the number of years to maturity.

In this case, the face value F is $22,000, the annual interest rater is 5.6% or 0.056 as a decimal, the interest is compounded semiannually, son = 2, and the time to maturity t is 11 years.

`\[PV = (22,000)/((1 + (0.056)/(2))^(2 * 11))\]`

Calculating this expression gives us the fair price
`(\(PV\))` of $14,735.95. This represents the present value of the future cash flows from the bond, taking into account the time value of money and the semiannual compounding of interest.

Investors use present value calculations to determine what they should be willing to pay for a bond based on its future cash flows. The lower fair price reflects the fact that the investor is paying less today for the future interest payments and the return of the face value due to the time value of money.