Question

yield to maturity-you are offered a 20year, 6% annual coupon bond with a face or par value of $1,000 at a price today, of $1,088.75. What rate of interest would you earn if you bought the bond and held it until maturity? That is, what is the YTM?

Answer 1

Solution:

The formula for calculating the yield to maturity of a bond is

YTM = [ C + ( ( F – P ) / N ) ] / [ ( F + P ) / 2 ]

Where C = Annual coupon Payment = ( Face value of the bond * Annual Coupon rate )

F = Face value of the bond    ;   P = Market price of the bond     ;   N = No. of years to maturity

As per the information given in the question

C =$ 1,000 * 6 % = $ 60 ;   F = $ 1,000   ; P = $ 1,088.75 ; N = 20

Applying the above values in the formula we have

= [ 60 + ( ( 1000 – 1088.75 ) / 20 ) ] / [ ( 1000 + 1088.75 ) / 2 ]

= [ 60 + ( - 88.75 / 20 ) ] / [ 2088.75 / 2 ]

= ( 60 - 4.4375 ) / 1044.375

= 55.5625 / 1044.375

= 0.0532

= 5.32 %

Thus the Yield to maturity ( YTM) of the bond is 5.32 %