$4-41$: It is now December $31,2021,$ and a jury just found in favour of a woman who sued the city

for injuries sustained in a January $2020$ accident. She requested recovery of lost wages, plus

$$250,000$ for pain and suffering, plus $$40,000$ for her 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 $$45,000$ in $2020,$ and her employer testified that she would

probably have received raises of $3\%$ per year. $($Assume for simplicity that the salary would have

been paid at year end.$)$ The actual payment will be made on December $31,2022.$ The judge

stipulated that all dollar amounts are to be adjusted to a present value basis on December $31,$

$2022,$ using a $7\%$ annual interest rate, using compound, not simple, interest. Furthermore, he

stipulated that the pain and suffering and legal expenses should be based on a December $31,$

$2021,$ date. How large a cheque must the city write on December $31,2022?|$

$*$Please include all steps and calculations, I$\text{'}$m using this to check my own work!$*$