need help with problem 8.1 (to the nearest penny)and 8.4(rounded to four decimal places)

Homework 8
Thursday, April 7th

Name:

8.1. The following are the current prices of zero-coupon bonds that have redemption value
\$1000:
Term to Maturity

Price

1
2
3

\$943.40
x
\$805.08

(a) If the one year forward rate deferred 1 year is 8%, determine x.
(b) Using these interest rates, determine the price of a bond that pays annual coupons of 40
and matures to 500 in three years.
8.2. The following are prices for zero-coupon bonds with redemption value of \$1, 000:
Term to Maturity

Price

1

\$943.40

2

\$898.47

3

\$847.62

4

\$792.16

Determine the one year forward rate starting in 2 years.
8.3. A company is obligated to pay a four year immediate annuity with annual payments of
\$2, 000 to a customer. There are only four assets available for investment: one and two year
zero coupon bonds, a three year 8% annual coupon bond, and a four year 6% annual coupon
bond. The company wants to exactly match its liabilities by purchasing these assets. The
bonds can be bought in any quantity, including fractional units. Determine the combined
price of the two zero coupon bonds that are purchased by this process given the following
spot rates:
Term (In Years)

Spot Rate

1

5.50%

2

5.85%

3

6.00%

4

6.35%

8.4. In a two year interest rate swap, the ?oating rate for each year is determined as the one
year rate at the beginning of the year, but payments are made at the end of the year. The
one year spot rate is 5%, and the two year spot rate is 6%. Find the approximate ?xed rate
for the two year swap.

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Homework 8

Book Problems:
Chapter 6: 1.1, 3.2, 3.6, and 4.1

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