Differential equations. Your employer automatically puts $10$ percent of your salary into a $401($k$)$ retirement account each year. The account earns $8\%$ interest. Suppose you just got the job, your starting salary is $$40000,$ and you expect to receive a $3\mathrm{.}5\%$ raise each year.

For simplicity, assume that interest earned and your raises are given as nominal rates and compound continuously.

Find the value of your retirement account after $30$ years