Question

Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000.

Maturity (Years)	Price
1	$	925.93
2		853.39
3		782.92
4		715.00
5		650.00

a. Calculate the forward rate of interest for each year. (Round your answers to 2 decimal places.)

b. How could you construct a 1-year forward loan beginning in year 3? (Round your Rate of synthetic loan answer to 1 decimal place.)

Face Value $
Rate on synthetic loan

c. How could you construct a 1-year forward loan beginning in year 4?

Face Value
Rate on synthetic loan

Answer 1

Question A.

Forward rate   = [ ( Current price / Future price ) - 1 ] *100

Year 2 = [ ( 925.93 / 853.39 ) - 1 ] * 100

           = 8.5%

Maturity	Price	Working	Forward rate
1	925.93	-	-
2	853.39	( 925.93 / 853.39 )	8.5%
3	782.92	( 853.39 / 782.92 )	9%
4	715.00	( 782.92 / 715.00 )	9.5%
5	650.00	( 715.00 / 650.00 )	10%

Question B.

3 Year zero coupon bond issue today , price at the maturity at year 3 = $782.92

Use this to buy bond next year = $782.92 / $715 = 1.095

Value at the end of year 3 = $1000

Value at the end of year 4 = $1000 * 1.095 = $1095

Rate of synthetic loan =   9.5%

Question C.

4 year zero coupon bond issue today , price at the maturity at the end of year 4 = $715

Use this to buy bond next year = $715 / $650 = 1.1

Value at the end of year 4 = $1000

Value at the end of year 5 = $1000 * 1.1 = $1100

Rate of synthetic loan =   10%