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Rule Your Numbers: Become a Financial Whiz in 10 Minutes Dr. Douglas Carlsen

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by Douglas Carlsen, DDS

THE RULE OF 72
Occasionally, while I drive about town, listening to local financial radio, a caller will ask about the Rule of 72. More often than not, the host “guru” will stutter something about “a complicated way to design investment strategy.” Please steer clear of these salesmen.

The Rule of 72 is simple. It calculates the approximate number of years it takes money to double by dividing 72 by the growth or interest rate, expressed as a percentage.

For instance, if you were to invest $100, compounding interest at a rate of nine percent per annum, the “rule of 72” gives 72/9 = eight years required for the investment to be worth $200. Similarly, to determine the time it takes for the value of money to halve at a given rate, divide 72 by that number. Thus at three percent inflation, it should take approximately 72/3 = 18 years for the value of a dollar to halve.

The above Rule of 72 gives an approximation of the time needed for something to double. For you math geeks, a more accurate calculation is as follows:

T= ln 2/ln (1+i)

T is the time period; i is the interest or growth rate; ln is the natural logarithm. Remember logs? Man, that seems like a different lifetime! Like back when we used slide rules and had to use hand instruments.

The real magic number is 69.3, yet 72 divides well with many numbers and is fairly accurate for rates up to 15 percent.

THE RULE OF 72 AND COMPOUND INTEREST
My stepson Scott inherited $75,000 at age 25 that he put it into a passively managed (no market timing) Vanguard IRA. With interest compounding with a 75/25 mix of stock to bond index funds, he expects to receive seven percent per year real growth (in 2012 dollars) over the next 40 years.1 This is the historical average after taking out inflation.

Using the Rule of 72, at seven percent per year, his money in real, or 2012 dollars, may double every 72/7=10 years.

At age 65, after 40 years, his $75,000 might double four times to $1,200,000 in today’s dollars.

As we’ll see, it is safe to withdraw four percent per year from an account forever without running out of money. That’s $48,000 income for life at age 65!

Scott has a huge head start for retirement, as long as he doesn’t touch the money for many years.

Interestingly, if Scott has a financial adviser actively manage his $75,000, his overall growth rate would normally be at least two percentage points lower, according to Larry Swedroe.2 He might expect five percent growth over those 40 years. 72/5 is approximately 14. His money would double three times instead of four, leaving him with $600,000 rather than $1,200,000. Yes, how your money is managed does make a difference over many years.

"MID-POINTING" TO FIND TOTAL LOAN INTEREST AND ESTIMATED PAYMENTS
Let’s envision a visit to an auto dealer, trade-in in tow, to purchase a new Lexus RX. Your trade-in is worth $10,000. You talk the sales person down to $40,000. The total amount of loan is therefore $30,000. The salesman says you may finance at six percent interest over six years.

Here’s how you can quickly approximate your loan payments to make sure there’s no dealer shenanigans. Take the mid-point of the loan total, in this case, $15,000. That’s your “average principle” during the term of the loan. Figure the total interest on that amount. In this case, six percent of $15,000 is $900. That’s what you’ll average in interest per year.

The loan is for six years, so total interest is $900 times six, or $5,400. Therefore, your total fee for the $30,000 loan is about $35,400. Divide by 72 months (six years) and you have payments of about $500 in your head, or $492 if you use a calculator. Either is close to the actual payments of $497 per month.

Note, the above is an approximation of real payments, yet if the dealer quotes a six year loan at six percent for $30K and comes back with $600 per month payments, you’ll know something’s wrong.

This mid-pointing method works well for practice loans, mortgages and any loan up to 30 years. Note that in real life, loans aren’t “straight line” as was calculated above, with the interest payments much heavier at the start of the loan. The above method does come up with reasonable results, though, for interest rates up to about 12 percent.

QUICK ONLINE AND MOBILE CALCULATORS (IF NUMBERS IN YOUR HEAD CAUSE ACUTE TORMENT)

Loan Calculators
Bankrate has an online mortgage calculator that can also be used for home, auto and practice loan calculations at www.bankrate.com/calculators/mortgages

For iPhone, use the free Zillow Real Estate Homes app.

Savings Calculators
For online savings calculations, go to www.bankrate.com/calculators/savings

For iPhone savings calculations, use the free MarkMoney app.

Combo Loan and Savings Calculators
For $3.99, MarkMoney has a loan and savings calculator app for iPhone.

THE FOUR PERCENT RULE
William Bengen provides a seminal study of safe withdrawal rates during retirement in Conserving Client Portfolios During Retirement.3 Bengen states that for taxed-deferred investments, it’s safe to take out up to 4.5 percent per year with yearly inflation increases without running out of money for 30-35 years. For after-tax funds, it’s a bit lower than four percent. Bottom line: Four percent withdrawals with yearly increase for inflation is almost always safe for retirees as long as one has at least 20 percent bonds and 20 percent stocks in one’s portfolio.

As I’ve indicated before, the average total savings needed for dentists who retire in their early to mid-60s is around $2,000,000. Using the four percent rule, a dentist may take out $80,000 per year safely for 30 years with a negligible chance of running out of money. Social Security, inheritance, sale of practice, and other variables often increase the yearly income total to between $125,000 and $175,000.

Interestingly, a dentist who retires at age 70 may not need $2,000,000 saved. Bengen shows on page 50 that for 20-25 years of retirement income, one can safely take out five percent per year. To get that $80,000 needed by an age 65 dentist, our 70-year-old only needs $1,600,000. Monte Carlo software programs often indicate that with well-diversified allocations, more than four percent is safe to withdraw. Please check with your adviser about what your safe withdrawal rate will be.

Yes, the four percent rule is very conservative, yet provides dentists a safe way to predict what they may spend in retirement.

I’ve come across several dentists with $5 million saved at age 60-65 who know they can live on around $150,000-$175,000 per year, yet are afraid $5 million isn’t enough. With the conservative four percent rule, they may have an income of at least $200,000 per year from savings with an additional $45,000+ from Social Security at their full retirement age.

I hope these quick tips make the financial morass out there a bit easier to negotiate.

References
  1. Annual Returns on Stock, T.Bonds and T.Bills: 1928 – 2011. From Federal Reserve database. It shows arithmetic mean of 11.2% annual growth for stocks and 5.4% for Treasury Bonds. Subtracting 3% annual inflation, we come up with 8.2% real return for stocks and 2.4% return for T-bonds. For a portfolio of 75% stocks and 25% bonds, we come up with an average return of 6.75%. Downloaded from http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histret.html on May 31, 2012

    Inflation from 1913 to 2011 is found to be 3.0% according to information at http://www.inflationdata.com/inflation/consumer_price_index/historicalcpi.aspx

  2. Larry Swedroe, The Only Guide to A Winning Investment Strategy You’ll Ever Need, Truman Talley Books, New York, NY, 2005, pg. 242.
  3. William Bengen, Conserving Client Portfolios During Retirement, FPA Press, Denver, CO, 2006.
Author's Bios
Douglas Carlsen, DDS, has delivered independent financial education to dentists since retiring from his practice in 2004 at age 53.

For Dentists’ Financial Newsletter, visit www.golichcarlsen.com and find the “newsletter” button at the bottom of the home page.

Additional Carlsen Dentaltown articles are at www.towniecentral.com. Search “Carlsen.” Videos available at www.youtube.com/user/DrDougCarlsen. Contact Dr. Carlsen at drcarlsen@gmail.com or 760-535-1621.
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