### More innumeracy

From an article about rich young doctors at the mag Medical Economics

"To have $1.5 million in a retirement plan by 65, a 35-year-old physician would have to consistently fund $42,000 each year," says Sherman L. Doll, a CPA and financial adviser from Walnut Creek, CA.Either that or Mr. Doll expects really bad returns from the market over the next 30 years. Think about it, if you contributed $42K/year for 30 years, your principal (and it is principal, not principle) would equal 1.26 million. According to my Excel based calculations (I don't have a calculator with logarithmic functions around) you'd need a whopping annual return of a bit under 1.2% to make it to 1.5 million. That is well under the real return of inflation-indexed treasury bonds.

It doesn't even matter if the market goes to hell in the first few years since you have plenty of time to earn it back. Even if the market went to zero at year 5 (that is you lost all you'd invested up till then) a modest 3% yearly return would get you to 1.5M. Hopefully, Mr. Doll was misquoted, otherwise I don't think I'd want him as my CPA.

## 2 Comments:

I haven't done the calculations as yet, but perhaps the model was putting the future amount in current dollas and assuming some absurd amount of hyperinflation?

:-)

Yes, Andy, I was misquoted. What I was trying to explain to the article author is the probability of having $1.5 million or more at age 65 given the following assumptions: fund $42K annually to a PS plan for 30 years, 70/30 diversified allocation of invested funds, and an annual return of 8.4% +/- 12.5%. The result is a 66% probability of having $1.5 million or more. But, that also means there's a 34% chance of having less than that figure. If you gotta have that much money at retirement, then a 34% error rate is pretty high. The error in your analysis is the use of an average rate of return and ignoring the volatility of returns. One might sail along with great returns and then have a string of loss years when the principal is highest. That can kill a portfolio. If you could choose when to take your bad years you'd choose the earlier years in the accumulation process.

The projections were created using Monte Carlo modeling software.

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