An individual is investing in a market where spot rates and forward rates apply.

In this market, if at time $t=0$ he agrees to invest $5\mathrm{.}5$ for two years, he will receive $6\mathrm{.}4$ at time $t=2$ years. Alternatively, if at time $t=0$ he agrees to invest $4\mathrm{.}5$ at time $t=1$ for either one year or two years, he will receive $7\mathrm{.}1$ or $8\mathrm{.}1$ at times $t=2$ and $t=3,$ respectively.

Calculate the price per $5,000$ nominal that the individual should pay for a fixed$-$interest bond bearing annual interest of $7\mathrm{.}2\%$ and is redeemable after $3$ years at $105\%.$ State your answer at $2$ decimal places.