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 $f_{1,k}$ refers to a forward rate for the period beginning in one

year and extending for $k$ years?

a$)f_{1,1}=$

b$)f_{1,3}=$

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

Hint: Use the equation $(1+r_1)(1+f_{1,k}{)}^k=(1+r_{k+1}{)}^{k+1}$ to solve for $f_{1,k}.$