# The Rule of 72

Do you want to know how long it will take to double your money?  Most investors do.  Are you interested in the expediential growth of your money?  Have you ever tried to calculate the rule of 72?

When I first started to read personal finance and investing books, I learned about the math behind what makes investing work.  The big driver behind what causes your money to grow is compound interest. While I was studying, the one theory that I kept coming across was the rule of 72.

The rule of 72 is just a basic mathematical formula.  It is used as a tool to help investors determine when they should expect to double the money they currently have invested.  The rule of 72 allows an investor to know when they should expect to double their money based on a forecasted rate of return.

Start by taking the projected rate that you expect your investment to return every year.  Divide that interest rate by 72. That will give you the number of years that it will take for you to double your money.

Example:

72 / 6% expected rate of return = 12 years to double your principal

72 / 8% expected rate of return = 9 years to double your principal

72 / 10% expected rate of return = 7.2 years to double your principal

The rule of 72 is what makes stocks a more attractive option than bonds or other fixed-income investments.  For example, the Vanguard 500 (VFINX) has returned 10.97% per year between the years 1976 and 2016.  Currently, the average interest rate on an FDIC insured savings account is slightly higher than1.15%. What is the difference between these two investments based on the rule of 72:

Vanguard 500 – 72 / 10.97 = 6.56 years to double your principal

Saving account (national average) – 72 / 1.15 = 62 years to double your principal

Over the coming decade, stocks are not expected to return 10% per year.  Currently, stocks are expensive investments and there is not much value to be found.  Jack Bogle who founded Vanguard and the first S&P 500 index fund that was available to individual investors predicts a more modest return of 6 or 7 percent for the coming decade.  Based on that forecast and the rule of 72, how long would it take to double an investment of \$3K in the Vanguard S&P 500 fund:

Vanguard 500 – 72 / 6.5% = 11 years to double your principal

When I started investing, I received a brochure from the investment company that provided me with a few charts on compound interest.  The chart showed how the rule of 72 worked with different interest rates. The brochure explained the wealth-building power of stocks vs more conservative investments based on the difference in long-term performance.  It also showed how it benefited an investor who had a few decades to take advantage of this powerful wealth building formula.

For example, a one-time investment of \$10K to grow in value to \$40K based on different interest rates:

• If an investor received a return of 3%, it would take 48 years for that \$10K to grow to \$40K
• If an investor received a return of 6%, the time would be reduced to 24 years to grow to \$40K
• If an investor received 12%, however, it would only take 12 years to grow \$10K to \$40K

What to do Now

What can investors do now to follow the rule of 72?  What are some alternatives since the S&P 500 is projected to underperform its historical average?  Is it possible to try to reduce the time it takes to double your money without taking on too much risk?  Here are some options that might help in doubling your money quicker:

Save more money.  By increasing your savings, you will double your money at a faster pace.  Try to increase your savings by 2-3% per year.

Go beyond the S&P 500.  Add a small-cap blend or extended market index fund that includes mid-cap stocks to your asset allocation.  Small-cap stocks have historically outperformed large-cap stocks. If you go with a 4:1 Ratio, you will emulate the total stock market.

Go beyond the United States for investing opportunities.  Add some international stocks to your portfolio. Add both developed nations and emerging markets for their growth potential.

Remember to keep some bonds in your portfolio.  Many experts are telling investors to stay away from bonds because of their current low yield and the raising interest rates.  Bonds have an opposite correlation than stocks. When stocks go down in value, bonds go up. By owning some bonds, you can buy stocks at a lower price when there is a stock market correction.

Conclusion

As an investor, you should keep the rule of 72 in the front of your mind.  You do not need to know the exact date as to when you will double your money.  From time-to-time, look at how your portfolio performed over the past 5 or 10 years to identify what your average rate of return is.  Apply the rule of 72 to know where you stand. If you are not satisfied with how long it is taking, look for ways to increase your returns that are within your risk tolerance.

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# How Bonds are Impacted by Interest Rates

There are many different economic factors that can change interest rates.  The Federal Reserve can act to change interest rates.  Interest rates can be lowered to increase borrowing and spending during a slumping economy.  Interest rates are also used to manage inflation.  No matter what causes the change in interest rates impact bonds.

The change has a direct impact on how bonds are priced.  When interest rates increase, the value of existing bonds decreases.  The opposite occurs when interest rates are reduced.  When that happens, the value of an existing bond would increase in value.

Not all bonds are the same.  Bonds have different maturity dates.  There are different issuers such as the Treasury, corporations, and municipalities.  Different bonds have different coupon rates.

With bonds, the value of a dollar today is worth more than a dollar tomorrow.  Today’s price of a bond is based on the total of future cash flows.  The value is discounted because they are not available today.  When there are changes in interest rates, all bonds are impacted.  Not all bonds, however, are impacted equally.

The price of a short-term bond is affected less by the increase in interest rates than a longer-term bond. Long-term bonds maturity value and interest are paid with future cash flows.  They are paid in the distant future.  When there is an increase in interest rates, the long-term bonds become discounted and decrease dramatically in value.

The interest rates are also known as the coupon rate that is periodically paid also impact the bond price volatility.  The higher the coupon rate, the more cash that is paid in interest to the investor prior to the maturity date.  When interest rates increase, the future cash flows are discounted at a higher rate.  The lower coupon bond will have more cash flow in the future.  The maturity value of the bond represents a larger portion of the total cash flow.  The current value of the bond will fall.

To determine the risk of a bond, an investor needs to look at maturity and coupon rates.  The most volatile bonds have lower coupons and longer maturities.  Less risky bonds are shorter until they reach maturity and have a high coupon rate.

Most individual investors use bonds to reduce the volatility of their overall portfolio and for income.  If you are using the bond portion of your asset allocation to reduce the overall volatility of your portfolio, consider bonds that have maturities that are shorter than five years.  Also, avoid zero-coupon bonds.

How much do bond prices change?  The prices of bonds do change, but not as drastically as with stocks.  What you can lose in bonds in one year, you can lose in stocks in one day.  Even though bonds are less volatile than stocks, it is still important to understand how interest rates affect them.

For example, assume that you have a bond with a 30-year maturity and a 6% coupon rate.  How much would the value of the bond change if there was a 2% drop in percentage points from 6% to 4%?  The bond would increase in value by almost 35%.  A bond that had a face value of \$500 prior to the interest rate decrease would climb to \$674.

What about if there was an increase in the interest rate from 6% to 8%.  The bond would decrease in value by almost 23%.  That \$500 bond would have a loss of \$113 in value.

The only way to reduce the price volatility of the bond portion of a portfolio is to consider shorter maturities.  When looking at mutual funds that invest in thousands of different bonds, look at the average maturity and the average coupon rate.  That will give you a ballpark of what the price volatility of the overall portfolio would be.  Below are a few examples of Vanguard Bond Funds:

Vanguard Total Bond Market Fund (VBMFX)

Average Maturity: 8.4 years

Average Coupon: 3%

Vanguard Long-Term Bond Index Fund (VBLTX)

Average Maturity: 24 years

Average Coupon: 4.4%

Vanguard Short-Term Bond Index Fund (VBIRX)

Average Maturity: 2.9 years

Average Coupon: 2%

Mutual fund managers keep a keen eye on interest rates and other economic factors.  They can adjust their portfolio by buying or selling bonds with shorten or longer maturities based on projected interest rate changes.  Fund managers are limited as to what they can buy and sell based on the fund’s investment objective statement found in the prospectus.  For example, a short-term fund cannot increase its holding in long-term bonds just because interest rates might be falling.

There is also a quality factor to consider.  When interest rates are increasing, lower-rated bonds tend to fall in price faster than high-quality bonds.  Bonds with a higher default risk fall the fastest.

If the economy was in a recession, a rise in interest rates would drop the price of a high-yield (junk) bond with a low rating.  A double or triple-A rated corporate bond with the same maturity would also fall in price, but not as quickly as the lower quality bond.  U.S. Government bonds have historically been rated as the highest quality bonds.

It is just as difficult to try to time changes in interest rates as it is to time the stock market.  There has been speculation of raising interest rates for many years and they are just starting to occur.  Economics and fund managers can make predictions as to where interest rates are heading, but nobody truly knows for sure.

When you are building the bond portion of your asset allocation, keep in mind why you are buying bonds.  Be aware how interest rates affect how bonds perform.  If you want to be more conservative, focus on high-quality government, corporate, and municipal bonds.  A risk-averse investor should also stick with short-term bonds or bond funds.

If you want to take on more risk, do so in the stock portion of your asset allocation.  That is not what bonds are intended for in an individual investor’s portfolio.  Bonds should be used to reduce risk and provide income, not add to the overall risk of a portfolio.

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