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. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Price				Maturity (years)			Yield to Maturity
$		450			20				%
$		550			20				%
$		550			10				%
$					10		10.50		%
$					10		7.50		%
$		450					8.50		%

Answer 1

1)

Number of periods = 20 * 2 = 40

Price = FV / (1 + r)ⁿ

450 = 1000 / (1 + r)⁴⁰

(1 + r)⁴⁰ = 2.22222

1 + r = 1.0202

r = 0.0202 or 2.02%

Yield to maturity = 2.02% * 2 = 4.03% or 4.04%

2)

Number of periods = 20 * 2 = 40

Price = FV / (1 + r)ⁿ

550 = 1000 / (1 + r)⁴⁰

(1 + r)⁴⁰ = 1.818182

1 + r = 1.01506

r = 0.01506 or 1.506%

Yield to maturity = 1.506% * 2 = 3.01%

3)

Number of periods = 10 * 2 = 20

Price = FV / (1 + r)ⁿ

550 = 1000 / (1 + r)²⁰

(1 + r)²⁰ = 1.818182

1 + r = 1.030343

r = 0.030343 or 3.0343%

Yield to maturity = 3.0343% * 2 = 6.07%

4)

Number of periods = 10 * 2 = 20

Rate = 10.5% / 2 = 5.25%

Price = FV / (1 + r)ⁿ

Price = 1000 / (1 + 0.0525)²⁰

Price = 1000 / 2.782544

Price = $359.38

5)

Number of periods = 10 * 2 = 20

Rate = 7.5% / 2 = 3.75%

Price = FV / (1 + r)ⁿ

Price = 1000 / (1 + 0.0375)²⁰

Price = 1000 / 2.088152

Price = $478.89

6)

Rate = 8.5% / 2 = 4.25%

Price = FV / (1 + r)ⁿ

450 = 1000 / (1 + 0.0425)ⁿ

(1 + 0.0425)ⁿ = 2.222222

n LN 1.0425 = LN 2.222222

n 0.041622 = 0.798508

n = 19.1847

Number of years = 19.1847 / 2

Number of years = 9.59 years