It is now December $31,2020($t $=0),$ and a jury just found in favor of a woman who sued the city for injuries sustained in a January $2019$ accident. She requested recovery of lost wages plus $$350,000$ for pain and suffering plus $$70,000$ for legal expenses. Her doctor testified that she has been unable to work since the accident and that she will not be able to work in the future. She is now $62,$ and the jury decided that she would have worked for another $3$ years. She was scheduled to have earned $$30,000$ in $2019.($To simplify this problem, assume that the entire annual salary amount would have been received on December $31,2019.)$ Her employer testified that she probably would have received raises of $3\%$ per year. The actual payment for the jury award will be made on December $31,2021.$ The judge stipulated that all dollar amounts are to be adjusted to a present value basis on December $31,2021,$ using a $7\%$ annual interest rate and using compound, not simple, interest. Furthermore, he stipulated that the pain and suffering and legal expenses should be based on a December $31,2020,$ date. How large a check must the city write on December $31,2021?$ Do not round intermediate calculations. Round your answer to the nearest dollar.