In today's market, you observe the following yield curve for government securities:

Maturity

$1$ year

$2$ years

$3$ years

$4$ years

$5$ years

$6$ years

$7$ years

$8$ years

$9$ years

$10$ years

Yield

$4\mathrm{.}00\%$

$4\mathrm{.}10$

$4\mathrm{.}30$

$4\mathrm{.}60$

$5\mathrm{.}00$

$5\mathrm{.}50$

$6\mathrm{.}10$

$6\mathrm{.}80$

$7\mathrm{.}60$

$8\mathrm{.}60$

Assume that the pure expectations hypothesis holds $($i$.$e$.,$ the maturity risk premium $=0).$

What does the market expect will be the interest rate on $2-$year securities five years from now? You may solve this problem using either the algebraic or geometric approach.

$04\mathrm{.}00\%$

$5\mathrm{.}55\%$

$6\mathrm{.}00\%$

$07\mathrm{.}45\%$

$8\mathrm{.}85\%$