Answer:
10.65%
Explanation:
To prevent arbitrage, investing in a 1-year security in each of the 1st, 2nd, 3rd and 4th years should yield the same return as investing in a 4-year security from the 1st year.
Accordingly,
[tex][(1+r_{1})(1+r_{2}) (1+r_{3})(1+r_{4})]^{\frac{1}{4}} = 1+R_{4}[/tex]
Where r = the 1-year rate of return for each given year
R = the 4-year rate of return
[tex][(1.03)(1.05) (1.065)(1+r_{4})]^{\frac{1}{4}} = 1.0625\\=1.151798(1+r_{4})=1.0625^{4} \\=1.151798(1+r_{4})=1.274429\\=(1+r_{4})=1.106469\\=r_{4}=0.106469[/tex]
Therefore, the expected one-year rate three years from now is 10.65%.
