Philippe is excited as he is considered a top performer at his place of employment and will receive a significant company bonus at the end of the month of $$20,000.$ He is looking to invest this money in his Tax$-$Free Savings Account $($TFSA$).$ He currently has TFSA contribution room of $$37,500$ and the contribution of his bonus would be the first time that he contributes. In addition, to contributing his company bonus, he is looking to invest $$400$ a month into his TFSA $($also starting at the end of the month when he gets his pay cheque$).$ Philippe expects a rate of $6\%$ compounded monthly and is wondering how much he will have after five years in his TFSA?

Show calculations for Philippe$$s total TFSA investment