Answer: 9.71%
Explanation:
The expected 1 year rate 2 years from now is given by;
[tex](1 + Rate_{2 years})^{2} * (1 + Rate_{1 year}) = (1 + Rate_{3 years})^{3}[/tex]
2 years rate = 8.20%
3 year rate = 8.7%
[tex](1 + Rate_{2 years})^{2} * (1 + Rate_{1 year}) = (1 + Rate_{3 years})^{3}[/tex]
[tex](1.082)^{2} * (1 + Rate_{1 year}) = (1.087)^{3}\\\\Rate_{1 year} = \frac{(1.087)^{3}}{(1.082)^{2}} - 1\\\\= \frac{1.284365503}{1.604588091037263424} - 1\\\\= 0.0971\\[/tex]
= 9.71%
