## Tuesday, April 9, 2013

### Doubling your money in a low rate environment

Question:  The interest rate is 2.0% per year forever.  You invest \$100 today.  How long does it take for your money to double?

Answer:  You will have \$200 at time t when

200=100x(1+0.02)t

Rearranging we get

2=1.02t

Taking logarithms and rearranging we get

t=ln(2)/ln(1.02) =(0.6931/0.0198) =35

We check this answer by plugging 35 into the first equation.  We get

199.98=100x(1.02)35

The difference between 199.98 and 200 is due to rounding.

When I was taught this problem a long time ago inflation and interest rates were both much larger and the problem was solved with an interest rate of 7.0%.  The answer at 7.0% is around 10.2 years.

A lot of economists are concerned about the impact of Fed policy on returns for savers, saving incentives, and investment decisions.  Allan Sloan recently wrote a nice article on how low interest rates are causing some investors to chase yield.  Certainly given a risk-free nominal return of 2.0% there is a large incentive to consider stocks.

Most economists are not highly concerned about inflation at this time.  However, even if you are not a monetarist there are reasons to be concerned about prolonged robust money growth.   Low returns cause investors to aggressively search for profitable investment opportunities.

Interested readers might want to look at my post on Allan Sloan’s article

http://financememos.com/2013/02/15/chasing-yield-by-investing-in-long-term-bonds/