Peter invested $$5000$ in an investment fund. Determine the accumulated value of his investment at the end of $8$ years if the interest rate was j$2=6\mathrm{.}5\%$ for the first $3$ years, j$4=6\mathrm{.}4\%$ for the next $4$ years and j$365=6\mathrm{.}3\%$ for the last year. What effective rate, j$,$ did he earn over the $8$ years?