Question

# Suppose that the prices of zero-coupon bonds with various maturities are given in the following table....

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 %

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%.

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