Question

The following is a list of prices for zero-coupon bonds of various maturities.

a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. (Do not round intermediate calculations. Round your answers to two decimal places.)

Maturity (years)	Price of Bond
1	$	955.90
2		916.47
3		834.12
4		766.39

b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. (Do not round intermediate calculations. Round your answers to two decimal places.)

Maturity (years)	Price of Bond
1	$	955.90
2		916.47
3		834.12
4		766.39

Maturity (years)	Price of Bond
2		916.47
3		834.12
4		766.39

Answer 1

Answer :

a) Here, we have that,

Sl. No.	Maturity years	Calculation	YTM
i)	One year	[ 1000 / 955.90 ] - 1	4.61%
ii)	Two years	[ 1000 / 916.47 ]^(1/2) - 1	4.46%
iii)	Three years	[ 1000 / 834.12 ]^(1/3) - 1	6.23%
iv)	Four years	[ 1000 / 766.39 ]^(1/4) - 1	6.88%

b) Here, we have that,

Sl. No.	Maturity years	Calculation	Forward Rate
i)	Second year	( 1 + 4.46% )^2 / ( 1 + 4.61%) - 1	4.31%
ii)	Third year	( 1 + 6.23% )^3 / ( 1 + 4.46% )^2 - 1	9.86%
iii)	Fourth year	( 1 + 6.88% )^4 / ( 1 + 6.23% )^3 - 1	8.85%