Question

A 5.5%, 5-year bond with semi-annual coupon payments and a face value of $1,000 has a market price of $1,032.19. Assume that the next coupon payment is exactly six months away. a) What is the yield-to-maturity of the bond? b) What is the effective annual rate implied by this price?

Answer 1

Information provided:

Time= 5 years*2= 10 semi-annual periods

Face value= future value= $1,000

Coupon rate= 5.50%/2= 2.75% per semi-annual period

Coupon payment= 0.0275*1,000= $27.50

Current price= present value= $1,032.19

a.The yield to maturity of the bond is calculated by entering the below in a financial calculator:

N= 10

FV= 1,000

PMT= 27.50

PV= -1,032.19

Press CPT and I/Y to compute the yield to maturity.

The value obtained is 2.3844%.

The yield to maturity is 2.3844%*2= 4.7688% 4.77%.

b.Effective annual rate is calculated by the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+ 0.0477/2)^2-1

        = 1.0483-1

        = 0.0483*100= 4.8269%

Therefore, the effective annual rate is 4.83%.

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