Interest rates on the market are starting to decrease. Ivan and Rubo are very happy because they invested some months ago into Government bonds.

In particular, Ivan owns a bond with these characteristics: maturity $5$ years and $7$ months, annual coupon $3\%.$ For Ivan's bond, risk$-$free interest rate is $2\%$ with spread of $1\mathrm{.}2\%($Government has a rating of BBB and requested spread for that rating notch is $1\mathrm{.}2\%)$

Rubo selected a 'longer' bond: maturity $6$ years and $2$ months, annual coupon $3\mathrm{.}5\%.$ Similarly, risk$-$free interest rate for Rubo's bond is $2\mathrm{.}25\%$ with spread of $1\mathrm{.}2\%$

Find:

$1)$ The equilibrium dirty and clean prices of the bonds

$2)$ The yield to maturity $($YTM$)$

$3)$ The duration and volatility

$4)$ If Rubo's bond can reach the price of $105$ in the future, and why

$5)$ If it is possible to create an arbitrage opportunity selling the bond with lowest YTM$,$ to buy the other one