Question

An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity equal to 8.2%. One bond, Bond C, pays an annual coupon of 10%; the other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 8.2% over the next 4 years, what will be the price of each of the bonds at the following time periods? Assume time 0 is today. Fill in the following table. Round your answers to the nearest cent.

T Price of Bond C Price of Bond Z
0 $
$
1
2
3
4

Answer 1

Explanation:

The price of Bond C at time t can be calculated using the formula:

P_C = (C / (1 + r)^t) + (F / (1 + r)^(n))

where C is the coupon payment, r is the yield to maturity, t is the time period, n is the number of years until maturity, and F is the face value.

Similarly, the price of Bond Z at time t can be calculated using the formula:

P_Z = F / (1 + r)^(n + t)

Substituting the values:

C = 100 (10% of $1,000)

r = 0.082

n = 4

F = $1,000

T Price of Bond C Price of Bond Z

0 $1,000 $1,000

1 $1,082 $961.67

2 $1,167.24 $926.58

3 $1,259.51 $893.63

4 $1,360.29 $862.54

The prices are rounded to the nearest cent.