## Friday, March 25, 2011

### FV - Future Value of Money and Doubling Rate

What is the Future Value of Money?

In Law School, one of the things our professors talked about in various economics related classes (tax law, trusts and estates, anti-trust, etc.) was FV or the Future Value of money.  As I noted in my Understanding Money post, what makes money complicated is that it exists in (at least) two dimensions - the first dimension being its value, and the second being time.  Time is the part that most people don't get - and as a result, simple things like loan interest and compound interest, mystify them.

My tax law professor used to bandy about the term FV, or Future Value of money.  If you have a dollar today, what is it worth in 10 years?  If invested properly, it should give you some rate of return and thus be worth more.  But of course, inflation is the spoiler in this party (and another time-based feature of money that most of us miss).

But in general, he used to use the rule-of-thumb that "money doubles in value about every seven years."  Seven years?  Is that realistic to expect in this day and age of 0.5% passbook savings?  Let's take a look.

Using our compound interest calculator, we find that, at:

1% Interest - money doubles in 70 years

2% Interest - money doubles in 35 years

3% Interest - money doubles in 23.5 years

4% Interest - money doubles in 17.5 years

5% Interest - money doubles in 14 years

6% Interest - money doubles in 12 years

7% Interest - money doubles in 10.25 years

8% Interest - money doubles in 9 years

9% Interest - money doubles in 8 years

10% Interest - money doubles in 7.25 years

11% Interest - money doubles in 6.6 years

12% Interest - money doubles in 6.15 years

Ouch.  Note that the low interest rates offered today by many banks are almost pointless.  You will never earn anything, in your lifetime, in terms of rate of return.  In order to get that fabled "double your money in seven years" you have to be looking at a 10% overall rate of return.  And there is only one place to do that, and that is in the stock market - if you are lucky.

Note also that the time to double money drops down as a decaying exponential, again, one of those "math thingies" that you "don't need to know in real life".  But what this means is that the fractional interest rates of today will never double the value of your money in your lifetime.  On the other hand, even a modest interest rate of 5-10% will easily double your investment within a fairly short period of time.  And what is even more interesting, is that really super-high interest rates, like 25%, 50% and 100% don't accelerate the process all that much (those rates double money in 3.15, 1.75 and 1 year, respectively).

In other words, if you can obtain a "reasonable" interest rate between 5-10%, you can expect to double your money in a fairly short period of time.  Anything lower than that is like watching paint dry.  Higher rates are faster, of course, but then again, are much harder to obtain and are quite risky.

What is interesting, of course, is that if you expect to "make money" on your investments, you need time for money to increase in value.  And if you want money to increase in value more quickly, you have to invest in riskier investments which have the potential to pay back more.

But, if you are getting closer and closer to retirement, well, you can't afford to "risk it all" to double-down your bet.  But that means, of course, that what you have in the bank won't grow much more than the rate of inflation.

This is why most investment advisers advise young people to put money in early and also take higher risks.  If you are young, you have more time to work with - and can afford to bounce back from bad investments as well.

A fairly conservatively invested portfolio should be able to return about a 7% rate of return over time - and thus double money every 10 years.  Perhaps this is an easier standard (and nice round number) to use than the 7 year standard my law professor used.  Thus, if you have \$100,000 invested in a mutual fund with a 7% rate of return, you should expect it to double in value in a decade, provided there is not a major market crash.

But, that also illustrates how many of us are now forced to invest in stocks these days, as stocks are "the only game in town" for the average person wanting to make more than a 2% rate of return.  And if you put ALL of your savings into low-return investments (1-2%) your portfolio will not appreciate much at all, over time - and in fact, fall behind, due to inflation.  While we actually had slight deflation during the economic crises of 2009, today, inflation is running about 2% (up slightly from last year).  So money in a 0.5% passbook savings account is actually worth less at the end of the year than at the start.

Again, this forces us to invest in more aggressive instruments, just to stay in place.  While you may "double your money" in 10 years, inflation has taken some of that money away from you, in terms of effective spending power.

And this is where planning for retirement gets tricky - and where most of us wake up at night and worry.  Yes, we can put aside a million bucks, over time, and retire a "millionaire".  But as history has shown, economic conditions can rapidly change the value of that money, to the point where it would hardly buy a cup of coffee.  Hyper-inflation can wipe out a carefully planned portfolio in short order.

Even more modest inflation, such as the double-digit inflation of the late 1970's, can be devastating to retirees.  Back then, most retirees were collecting Social Security or a Pension Plan.  The former has a cost-of-living adjustment, while the latter pays out the same amount (and some even have cost-of-living adjustments), regardless of market values of stocks.  The 401(k) and IRA had jut been invented, and no one had yet to retire on them.

For our generation, things will be different.  We have to hope that our money will get a good rate of return without risking it all.  We have to hope that inflation will remain relatively modest as well.  And we have to set aside as much money as we can, so that we don't "run out" in retirement.

There are many variables in the equation, with savings being the only thing we have control over.  For our generation, the retirement years will not be as easy and carefree as the defined-benefit pension plan generation.

Unfair? Perhaps.  But the defined-benefit pensions were probably not sustainable (as GM and School Districts found out or are finding out).  And as I have noted before, you can rail about the unfairness of it all, or take action the best you can.  Cutting expenses and saving money, in the long run, is really your only choice.