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 %

Homework Answers

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%.

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