On January $1,1988,$ Felix inherited a perpetuity with annual payments beginning in six months. The first payment was $$5,000,$ and after that the payments increased by $4\%$ each year. Find the value of this perpetuity on January $1,1995$ if the annual effective interest rate was $7\%$ from January $1,1988$ through January $1,1996$ and $6\%$ thereafter. $($Round your answer to the nearest cent.$)$ answer is $$389486\mathrm{.}63.$ please show work