Emily has borrowed $$1000000$ from MQ Bank for $10$ years at an interest rate of j$2=4\mathrm{.}1\%$ p$.$a$.$ She will make $10$ annual repayments. According to the loan agreement, Emily's repayments will be $$87000$ for the first two years followed by payments of X per year for the remaining eight years. This loan needs to be fully repaid by the end of $10$ years.

$($a$)$ Assume that all annual repayments will be paid at the end of each year $($the first payment will be at the end of the first year$),$ what is the value of Emily's annual payment amount, X $($rounded to four decimal places$)?$ The correct answer is: $135498\mathrm{.}8246$