Question

Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000. Use semi-annual periods.

Price	Maturity (years)	Yield to Maturity
$490	20		%
$590	20		%
$590	10		%
	10	10.90	%
	10	7.10	%
$490		8.90	%

Answer 1

a). r = [FV/PV]^1/n - 1

= [$1,000 / $490]^1/40 - 1 = 1.0180 - 1 = 0.0180, or 1.80%

YTM = 2r = 2 x 1.80% = 3.60%

b). r = [FV/PV]^1/n - 1

= [$1,000 / $590]^1/40 - 1 = 1.0133 - 1 = 0.0133, or 1.33%

YTM = 2r = 2 x 1.33% = 2.66%

c). r = [FV/PV]^1/n - 1

= [$1,000 / $590]^1/20 - 1 = 1.0267 - 1 = 0.0267, or 2.67%

YTM = 2r = 2 x 2.67% = 5.35%

d). PV = FV / (1 + r)ⁿ

= $1,000 / [1 + (0.1090/2)]²⁰ = $1,000 / 2.8902 = $345.99

e). PV = FV / (1 + r)ⁿ

= $1,000 / [1 + (0.0710/2)]²⁰ = $1,000 / 2.0091 = $497.73

f). n = [ln(FV / PV)] / [ln(1 + r)]

= (1/2) x [ln($1,000 / $490)] / [ln{1 + (0.0890 / 2)}]

= (1/2) x [ln2.0408] / [ln1.0445]

= (1/2) x [0.7133 / 0.0435] = (1/2) x 16.38 = 8.19 years