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: (2 marks)
Step 1: Calculate the future value of the company bonus after five years
FV = PV(1 + r/n)^(nt)
FV = $20,000(1 + 0.06/12)^(12*5)
FV = $20,000(1 + 0.005)^60
FV = $20,000(1.348009)
FV = $26,960.18
Step 2: Calculate the future value of the monthly contributions after five years
Using the future value of an annuity formula:
FV = PMT[((1 + r/n)^(nt) - 1)/(r/n)]
FV = $400[((1 + 0.06/12)^(12*5) - 1)/(0.06/12)]
FV = $400[(1.348009 - 1)/(0.005)]
FV = $400(0.348009/0.005)
FV = $27,840.72
Step 3: Calculate the total investment in the TFSA after five years
Total TFSA = FV(company bonus) + FV(monthly contributions)
Total TFSA = $26,960.18 + $27,840.72
Total TFSA = $54,800.90
Therefore, Philippe will have approximately $54,800.90 in his TFSA after five years.