Your father has discovered that you're taking a finance course and has asked you to estimate how much he should be saving for your little sister Sofia's education. He gives you the following information:

Sofia will be entering university for a $4-$year degree in exactly $12$ years' time. At that time, college fees will be $$40,000$ per year, increasing at a rate of $3\%$ per year. College payments are due at the beginning of the school year, and the first payment will be made in $12$ years, starting the day after your father opens Sofia's account. Your father will invest annually $($at the end of each year$)$ in an account today, with a nominal rate of $6\%$ and annual compounding. Finally, Sofia's aunt promises to deposit $$5,000$ in the account when Sofia turns $16,$ in exactly $10$ years $($a single deposit from her aunt$).$ The last payment your dad makes will be on the day of Sofia's first tuition payment.

The question is: how much would your father need to deposit each year for the next $12$ years to be able to send Sofia to university?