r 1 = 5.4% r 2 = 5.9% r 3 = 6.6% r 4 = 7.4% What are the following forward rates

Question

           r1 = 5.4%    r2 = 5.9%     r3 = 6.6%     r4 = 7.4%

What are the following forward rates, where f1, k refers to a forward rate for the period beginning in one year and extending for k years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Consider the following spot interest rates for maturities of one, two, three, and four years.

           r1 = 5.4%    r2 = 5.9%     r3 = 6.6%     r4 = 7.4%

What are the following forward rates, where f1, k refers to a forward rate for the period beginning in one year and extending for k years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

F1 = [(1+r2)^2 /(1+r1)^1 ] - 1

         = [(1+.059)^2 /(1+.054) - 1]

           = [1.12148 / 1.054] - 1

             = 1.0640-1

              = .0640 or 6.40%

F2 = [(1+.066)^3 /(1+.059)^2 ] - 1

      = [(1.066)^3 /(1+.059)^2 ]   - 1

         =[ 1.21136 / 1.12148] - 1

       = 1.0801-1

       = .0801 or 8.01%

F3= [(1+.074)^4/ (1+.066)^3 ] -1

     = [(1.074)^4 /(1.066)^3 ] -1

     = [1.33051/ 1.21136] - 1

      = 1.0984-1

         = .0984 or 9.84%

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