Consider the following spot interest rates for maturities of one, two, three, and four years.

$r_1=4\mathrm{.}1\%$

$r_2=4\mathrm{.}9\%$

$r_3=5\mathrm{.}6\%$

$r_4=6\mathrm{.}5\%$

What are the following forward rates, where $f_{k,1}$ refers to a forward rate beginning in $k$ years and

extending for $1$ year?

a$).f_{2,1}=?$

b$).f_{3,1}=$

$($Note: Express your answer in percentages; round your answer to four decimal places.$)$

Hint: Use the equation $(1+r_k{)}^k(1+f_{k,1})=(1+r_{k+1}{)}^{k+1}$ to solve for $f_{k,1}.$