Answer:
a. 8.37%
b. $942.96 or
Explanation:
If a bond is held until maturity, the total return expected from the bond until maturity is known as Yield to maturity. It is considered as long term and expressed in annual term.
a.
Yield to maturity = [ C + ( ( F - P ) / n ) ] / [ ( F + P ) / 2 ]
Where
C = Coupon payment = 1,000 x 8.7% = 87 annually = 43.5 semiannually
F = Face value = $1,000
P = Price of bond = $1,035.37
n = number of periods = 2 per year x 10 year = 20 periods
Yield to maturity = [ C + ( ( F - P ) / n ) ] / [ ( F + P ) / 2 ]
Yield to maturity = [ 43.5 + ( ( 1,000 - 1035.37 ) / 20 ) ] / [ ( 1,000 + 1035.37 ) / 2 ]
Yield to maturity = 41.73 / 1017.69
Yield to maturity = 0.041 = 4.10% = 4.1% semiannually ( rounded off to 1 decimal place)
Annual YTM compounding semiannually = [ ( 1 + 4.1% )^2 ] -1 = 0.0837 = 8.37%
b.
Price of Bond = C x [ ( ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Price of Bond = 43.5 x [ ( ( 1 - ( 1 + 0.48 )^-20 ) / 0.048 ] + [ 1,000 / ( 1 + 0.048 )^20 ]
Price of Bond = 551.42 + 391.54 = $942.96
