Let's all make a retirement plan. As our base assumption, let's assume civilization holds together and the stock market continues to return about 7% on average, in the long run.

Nobody just saves money one time. Suppose you have a constant annual income of of which you manage to save 20%. Assume your investment is a continuous flow into the stock market. (This is definitely not true, but again, close enough.) Starting from 0, how long to save $1,000,000, in terms of ?

How does this performance compare to my brother-in-law, who is so risk averse he keeps all his savings in a checking account?

Finally, what if your income grows by 3% per year over time, starting from annually after you finish college? Note: For this one, let's finally stop assuming income growth is continuously compounded, we certainly don't get a raise every minute of the day...But it's not too bad to assume our income after t years has been increased by a factor of 1.03t (even though this is only really true for integer t , at least our income will be just right once per year) Now 1.03=eln1.03 so this is equivalent to continuously compounded growth with k=ln1.03.02956, rather than the .03 we would've gotten from continuous compounding. It didn't matter much after all!

What starting income do you need to be able to retire at your preferred age?