323.14

"Invest early and often." You often hear that, but why does it make sense? Consider two outcomes of your life: (1) you invest $5000 per year in the stock market, starting when you’re 25, or (2) you invest $10,000 per year in the stock market starting when you’re 35. The average annual return on the stock market is 12%. How much more or less will you have when you're 65 with the second path vs. the first path? (8)

These are two annuities. We’re comparing the future values of these two annuities. Since they both will end when we’re 65, we do not have to worry about the fact that they start at different times (except to note that the second annuity is shorter.)

In class, we computed the FV of an annuity by computing its PV and then the FV of the PV. So here it goes:

So even if you invest twice as much starting only 10 years later, you’ll be $1,422,220.26 poorer when you retire if you take the second path for your life. How do you like them apples?!

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