Question

At maturity, each of the following zero coupon bonds (pure discount bonds) will be worth $1,000. For each bond, fill in the missing quantity in the following table. Assume semi-annual compounding. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answers to 2 decimal places, e.g. 15.25 or 15.25%.)

		Price		Maturity (years)		Yield to maturity
A		$445		8		???	%
B		$405		???		7	%
C		???		15		11	%

Answer 1

Face Value Zero-coupon Bond = $1000

A). Price = $445

Calculating the Semi-annual YTm of Xero-coupon Bond:-

where, n = no of periods = 8 years*2 = 20

Semi-Annual YTM = 5.1907%

Annual YTM = 5.1907%*2

Annual YTM = 10.38%

B). Current Market Rate(YTM) = 7%

Calculating the Price of Zero-coupon Bond:-

where, r = Semi-annual YTM = 7%/2 = 3.5%

n = no of periods

(1.035)^n = 2.46913580246

Taking Log on both sides,

n*Log(1.035) = Log(2.46913580246)

n*0.014940350= 0.3925449768

n = 26.27

No of years to maturity = 26.27/2 = 13.14 years

c). Face Value Zero-coupon Bond = $1000

Current Market Rate(YTM) = 15%

Calculating the Price of Zero-coupon Bond:-

where, r = Semi-annual YTM = 11%/2 = 5.50%

n = no of periods = 15 years*2 = 30

Price = $200.64

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