The value of the bond that matures in 20 years, makes an annual coupon payment of $40, and has a par value of $1,000 is approximately $440.
To determine the bond's value, apply the formula for the present value of a bond, which is expressed as
PV = C * (1 - (1+r)⁻ⁿ)/r + F/(1+r)ⁿ
Here, PV signifies the present value, C is the annual coupon payment, r represents the required rate of return, n denotes the number of years until maturity, and F stands for the par value of the bond.
Insert the provided values into the formula.
Specifically, for this instance, C = $40, r = 0.10, n = 20, and F = $1000. Execute the calculation using the formula:
PV = $40 * (1 - (1+0.10)⁻²⁰)/0.10 + $1000/(1+0.10)²⁰
= $437.24.
To ensure simplicity, round the answer to the nearest $10. Consequently, the approximate value of the bond is $440.
Complete Question
Determine the worth of a bond with a maturity period of 20 years, an annual coupon payment of $40, and a face value of $1,000. Assuming a required rate of return of 10%, round your answer to the nearest $10.