Question

8 What is the yield to maturity of a bond if it is sold for $1,029.33, pays a semiannual coupon of $40, and matures in 15 years? 0 3.83% O 1.92% O 8.10% 04.05% O 7.67%

Answer 1

The Approximate Yield to Maturity Formula =[Coupon + ( Face Value - Market Price) / Number of years to maturity] / [( Face Value + Market Price)/2 ] *100

= [$ 40+ ( $ 1,000- $ 1029.33) /(15*2)] /[( $ 1,000+ $ 1029.33)/2] *100

= 39.0223/1014.665*100

= 3.84583089%

Annual YTM = 3.84583089% * 2

= 7.69%

Note : Semi Annual Coupon = $ 40

Annual Coupon = $ 40*2

= $ 80

Hence Rate = $80 /$ 1000*100

= 8%

Since this formula gives an approximate value, The financial calculators can be used alternatively.

where,

Par Value = $ 1,000

Market Price = $  1029.33

Annual rate = 8%

Payments = 2

Maturity in Years = 15 Years

Hence the yield to maturity = 7.67%

Answer = 7.67%