Problem #$5$: The function $s(t)=0\mathrm{.}15-0\mathrm{.}03e^{-\frac{t}{4}}$ provides the term structure of effective annual rates of zero coupon bonds of

maturity $t,$ with $t$ in years. Find the following:

$($a$)$ The effective annual rate of a $3$ year zero coupon bond.

$($b$)$ The $2-$year forward effective annual rate for a one year period.

$($c$)$ The forward effective annual rate for a one year period, $3$ years forward.

$($d$)$ The $3-$year forward effective annual rate for a $3$ month period.

$($e$)$ The forward effective annual rate for a one day period, $3$ years forward $($the "overnight" rate$).$

$($Use $\frac{1}{365}$ for a one$-$day period.$)$

Problem $=5(a)$ :

Problem $=5(b)$ :

Problem $=5(c)$ :

Problem $=5($d$)$:

Problem $=5(e)$:

Answer as a percentage,

correct to $2$ decimals.

Answer as a percentage,

correct to $2$ decimals.

Answer as a percentage,

correct to $2$ decimals.

Answer as a percentage,

correct to $2$ decimals.

Answer as a percentage,

correct to $2$ decimals.