Suppose that the one-year interest rate over the next four years is expected to be 2%,...
Suppose that the one-year interest rate over the next four years is expected to be 2%, 3%, 4% and 6%.
a) Find the interest rate on a three- year bond.
b) Find the interest rate on a four-year bond
c) Find the interest rate on a four -year bond when the liquidity premium of the investor to hold a four-year bond is 2%.
PLEASE SHOW YOUR WORK ON HOW YOU GOT EACH ANSWER (INCLUDING STEP-BY-STEP CALCULATIONS)!
Homework Answers
(a) 1-Year rate at present = r1 = 2%, 1-year rate 1-year from now = 1f1 = 3%, 1-year rate 2-years from now = 1f2 = 4% and 1-year rate 3-years from now = 1f3 = 6%
Interest Rate on 3-year bond = [(1+r1) x (1+1f) x (1+1f2)]^(1/3) - 1 = [(1.02) x (1.03) x (1.04)]^(1/3) - 1 = 0.02997 or 2.997 %
(b) Interest Rate on 4-year bond = [(1+r1) x (1+1f) x (1+1f2) x (1+1f3)]^(1/4) - 1 = [(1.02) x (1.03) x (1.04) x (1.06)]^(1/4) - 1 = 0.03739 or 3.739%
(c) The Interest Rate on 4-year bond is 3.739% without the liquidity premium. Liquidity Premium is added to the interest rate to account for the bond's liquidity.
Liquidity premium = 2 %
Overall Interest Rate on 4-year bond = 3.739 + 2 = 5.739%
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