r 1 = 6.2% r 2 = 6.7% r 3 = 7.4% r 4 = 8.2% What are the following forward rates

Question

           r1 = 6.2%    r2 = 6.7%     r3 = 7.4%     r4 = 8.2%

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.)

f1,1 %

f1,2 %

  f1,3 %
hint Use the equation (1 + r1)(1 + f1, k)k = (1 + rk+1)k+1 to solve for f1, k.

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

           r1 = 6.2%    r2 = 6.7%     r3 = 7.4%     r4 = 8.2%

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.)

f1,1 %

f1,2 %

  f1,3 %
hint Use the equation (1 + r1)(1 + f1, k)k = (1 + rk+1)k+1 to solve for f1, k.

Explanation / Answer

1)

f1,1 = (1+ r2)^2/(1+r1) - 1

f1,1 = (1+6.7%)^2/(1+6.2%) -1

f1,1 = 7.20%

2)

f1,2 = ((1+ r3)^3/(1+r1))^(1/2) - 1

f1,2 = ((1+7.4%)^3/(1+6.2%))^(1/2) - 1

f1,2 = 8.01%

3)

  f1,3 =  ((1+ r4)^4/(1+r1))^(1/3) - 1

f1,3 =  ((1+8.2%)^4/(1+6.2%))^(1/3) - 1

f1,3 = 8.88%

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