A 20-year maturity bond with par value of $1,000 makes semiannual coupon payments at a coupon rate of 8%. Find the bond equivalent and effective annual yield to maturity of the bond for the following bond prices.
a. $940.
b. $1,000.
c. $1,060.

a. At  $940, Effective annual yield to maturity is 8.64 %

b. At  $1,000, Effective annual yield to maturity is 8 %

c. At $1,060, Effective annual yield to maturity is 7.42%

Explanation:

Part a. Effective annual yield to maturity of the bond at bond price of $940.

PV = - $940

N = 20 × 2 = 40

PMT = 1000 × 8% × (1/2) = $ 40

FV = $1,000

YTM = 4.3176

Therefore Effective annual yield to maturity is 4.3176 × 2 = 8.64 %

Part b. Effective annual yield to maturity of the bond at bond price of $1,000.

PV = - $1,000

N = 20 × 2 = 40

PMT = 1000 × 8% × (1/2) = $ 40

FV = $1,000

YTM = 4.00

Therefore Effective annual yield to maturity is  4.00 × 2 = 8 %

Part c. Effective annual yield to maturity of the bond at bond price of $1,060.

PV = - $1,060

N = 20 × 2 = 40

PMT = 1000 × 8% × (1/2) = $ 40

FV = $1,000

YTM = 3.7098

Therefore Effective annual yield to maturity is 3.7098 × 2 = 7.42%

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