Celine is currently 24 years old and plans to retire on her 64th Birthday. She anticipates her annual living expenses to be $50,000, inflation-adjusted, and her life expectancy is 95. She plans to save a fixed amount every year in an RRSP account to benefit from its tax deferrals. In addition, she plans, while she is working, to invest her money in a broad market, low-fee, indexed fund, with an average rate of return of 10% per year and volatility of 15%. Upon retirement, she plans to move her money to a GIC account with a 3% annual rate of return. She anticipates she needs to pay 15% tax on her retirement withdrawals and the inflation rate is 2% per year.
a. How much should she contribute to the RRSP account, at the end of each year, so that she would be able to consume the equivalent of $50K, after-tax deductions, at beginning of each year in her retirement? In this part, ignore the risk of the indexed fund and work only with its average return value. (clarification: the first and last deposits to the account are on her 25th and 64th birthdays. The first and last withdrawals are on the first day after her 64th and 94th birthdays). Your output excel sheet (and the Python DataFrame) should have at least three columns: Age of your client (from 25 to 94), annual deposit/withdrawal at each year, and the account balance at the end of each year.
b. Next, consider the risk of the investment in the indexed fund. Simulate annual returns for the investment horizon and find the realized balance at the end of each year, using the discrete-time compounding. Save these values in a new column to the above excel sheet. Run the simulations 20 times. For simplicity allow the account balance to be negative. But make sure in that case, there will be no more interest gained from the GIC account. From these 20 simulations, find the average value of the account balance each year. Plot this series and the account balance in part (a) together on a plot, use the age of the client as the x-axis labels. a
