Question

#5) 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		$441		10		???	%
B		$409		???		5	%
C		???		15		13	%

Answer 1

Face Value Zero-coupon Bond = $1000

A). Price = $441

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

where, n = no of periods = 10 years*2 = 20

Semi-Annual YTM = 4.17849%

Annual YTM = 4.17849%*2

Annual YTM = 8.36%

B). Current Market Rate(YTM) = 5%

Calculating the Price of Zero-coupon Bond:-

where, r = Semi-annual YTM = 5%/2 = 2.5%

n = no of periods

(1.025)^n = 2.44498777506

Taking Log on both sides,

n*Log(1.025) = Log(2.44498777506)

n*0.0107238654 = 0.388276692

n = 36.2068

No of years to maturity = 36.2068/2 = 18.10 years

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

Current Market Rate(YTM) = 13%

Calculating the Price of Zero-coupon Bond:-

where, r = Semi-annual YTM = 13%/2 = 6.50%

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

Price = $151.19

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