Saving for Retirement

Assume an investor begins saving for retirement at age $25$ and retires at age $65.$ Each year, she

contributes $$10,000$ to her retirement account. To keep things simple, assume that there are $40$

annual contributions that occur on the investor's $25-$th$,26-$th$,$ dots,$64-$th birthdays, and that the

final retirement wealth is determined on the investor's $65-$th birthday. ${?}^1$ Savings are invested as

follows: $50\%$ in a broad stock market index and $50\%$ in T$-$Bills.

Your task is to compute the accumulated real retirement savings at age $65$ for different return

realizations. As explained below, you will generate returns using a Monte Carlo simulation. On

Canvas, you can find an Excel file containing historical net returns on the S&P $500$ and $3-$month

T$-$bills, as well as the consumer price index $($CPI$)$ from $1926$ to $2017.$ The return on the CPI

serves as a measure of inflation.

STEPS:

Compute the annual real return on the $\frac{50}{50}$ portfolio for each year in the sample. The

resulting set of $92$ portfolio returns represents the empirical distribution. These are the

returns investors historically realized when investing in a $\frac{50}{50}$mix of stocks and T$-$bills