Question

b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. (Do not round intermediate calculations. Round your answers to two decimal places.) Maturity (years) Price of Bond $ 1 955.00 2 901.47 838.62 3 4 779.89 Maturity (Years) Price of Bond Forward Rate $ 901.47 2 838.62 $ 779.89 4

Answer 1

Assuming Face value of $1,000 we can calculate spot rate as follows:

955 = 1000/ (1 + x1) ^ 1

x1 = 4.71%

Hence, x(1,1) = 4.71%

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901.47 = 1000 / (1 + x2) ^ 2

x2 = 5.32%

(1 + x2) ^ 2 = (1 + x(1,1))(1+x(2,1))

1.0532^2 = 1.0471 * (1+x(2,1))

Hence x(2,1) = 5.94%

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838.62 = 1000 / (1 + x3)^3

x3 = 6.04%

(1 + x3)^3 = (1 +x(1,1))(1+x(2,1))(1+x(3,1))

1.0604^3 = 1.0471 * 1.0594* (1+x(3,1))

x(3,1) = 7.49%

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779.89 = 1000 / (1 + x4) ^4

x4 = 6.41%

(1 + x4) ^4 = (1 +x(1,1))(1+x(2,1))(1+x(3,1))(1+x(4,1))

x(4,1) = 7.53%