The following table shows some data for three zero-coupon bonds. The face value of each bond is $1,000.

The following table shows some data for three zero-coupon bonds. The face value of each bond is $1,000.


Bond     Price     Maturity (Years)     Yield to Maturity
A     $     310                 25                 —    
B           310                 —                 9     %
C           —                 11                 8    



a. What is the yield to maturity of bond A? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places. Assume annual compounding.)





b. What is the maturity of B? (Do not round intermediate calculations. Round your answer to 2 decimal places. Assume annual compounding.)

 



c. What is the price of C? (Do not round intermediate calculations. Round your answer to 2 decimal places. Assume annual compounding.)






Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

The general bond formula is:
Bond price = PV of coupon payments + PV of face value
With a zero-coupon bond and annual compounding, the formula is reduced to:

Bond price	=	PV of face value
Bond price	=	FV / (1 + r)t

a.

Bond price	=	FV / (1 + r)t
$310	=	$1,000 / (1 + r)25
(1 + r)25	=	$1,000 / $310
r	=	3.2258(1 / 25) – 1
r	=	.0480, or 4.796%

b.

Bond price	=	FV / (1 + r)t
$310	=	$1,000 / 1.09t
1.09t	=	$1,000 / $310
t × ln1.09	=	ln.0480
t	=	ln.0480 / ln1.09
t	=	13.59 years

c.

Bond price	=	FV / (1 + r)t
	=	$1,000 / 1.0811
	=	$428.88

Calculator computations:
a.

Enter

25

–310

1,000

N

I/Y

PV

PMT

FV

Solve for

4.796

 
b.

Enter

9

–310

1,000

N

I/Y

PV

PMT

FV

Solve for

13.59

 
c.

Enter

11

8

–1,000

N

I/Y

PV

PMT

FV

Solve for

428.88