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	$	974.68
2		903.39
3		842.92
4		783.00
5		669.92

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

Maturity (years)	Forward rate
2	%
3	%
4	%
5	%

b. How could you construct a 1-year forward loan beginning in year 3? (Round your Rate of synthetic loan answer to 2 decimal places.)

Face value
Rate if synthetic loan	%

c. How could you construct a 1-year forward loan beginning in year 4? (Round your answers to 2 decimal places.)

Face value
Rate if synthetic loan	%

Answer 1

Answer :

a) Forward rate = [ ( current price / future price ) - 1 ] * 100

Maturity	Price	Working	Forward rate
1	974.68	-	-
2	903.39	( 974.68 / 903.39 ) - 1	7.89%
3	842.92	( 903.39 / 842.92 ) - 1	7.17%
4	783.00	( 842.92 / 783.00 ) - 1	7.65%
5	669.92	( 783.00 / 669.92 ) - 1	16.88%

b) 3 year zero coupon bond issue today, price at the maturity at year 3 = $ 842.92

Use this to buy bond next year = $ 842.92 / $ 783.00 = 1.07653

Value at the end of year 3 = $ 1000

Value at the end of year 4 = $ 1000 * 1.0765 = $ 1,076.53

Rate of synthetic loan = 7.65%

c)  4 year zero coupon bond issue today, price at the maturity at year 4 = $ 783.00

   Use this to buy bond next year = $ 783.00 / $ 669.92 = 1.16879

Value at the end of year 4 = $ 1000

Value at the end of year 5 = $ 1000 * 1.1688 = $ 1,168.80

Rate of synthetic loan = 16.88%.