Question

Based on economists’ forecasts and analysis, one-year T-bill rates and liquidity premiums for the next four years are expected to be as follows: 1R1 = .50% E(2r1) = .75% L2 = 0.07% E(3r1) = .85% L3 = 0.16% E(4r1) = 1.15% L4 = 0.17% Identify the four annual rates. (Round your answers to 2 decimal places. (e.g., 32.16)) Annual Rates Year 1 .5 % Year 2 % Year 3 % Year 4 %

Answer 1

Annual Rate = [(1 + r₁)x(1 + r₂)x....x(1 + r_n)]^1/n - 1

Year 1 = [1.005) - 1 = 0.50%

Year 2 = [(1.0050)(1.0075 + 0.0007)]^1/2 -1 = [(1.0050)(1.0082)]^1/2 -1 = 1.0066 - 1 = 0.0066, or 0.66%

Year 3 = [(1.0050)(1.0075 + 0.0007)(1.0085 + 0.0016)]^1/3 -1 = [(1.0050)(1.0082)(1.0101)]^1/3 -1

= 1.0079 - 1 = 0.0079, or 0.79%

Year 4 = [(1.0050)(1.0075 + 0.0007)(1.0085 + 0.0016)(1.0115 + 0.0017)]^1/4 -1

= [(1.0050)(1.0082)(1.0101)(1.0132)]^1/4 -1 = 1.0091 - 1 = 0.0091, or 0.91%