| Yearly Interest Rate | Number of years | ||||
|---|---|---|---|---|---|
| 5 | 10 | 20 | 30 | 40 | |
| 0.02 | 1.10 | 1.22 | 1.49 | 1.81 | 2.21 |
| 0.04 | 1.22 | 1.48 | 2.19 | 3.24 | 4.80 |
| 0.06 | 1.34 | 1.79 | 3.21 | 5.74 | 10.29 |
| 0.08 | 1.47 | 2.16 | 4.66 | 10.06 | 21.72 |
| 0.10 | 1.61 | 2.59 | 6.73 | 17.45 | 45.26 |
| 0.20 | 2.49 | 6.19 | 38.34 | 237.38 | 1,469.77 |
| 0.30 | 3.71 | 13.79 | 190.05 | 2,620.00 | 36,118.86 |
| 0.40 | 5.38 | 28.93 | 836.68 | 24,201.43 | 700,037.70 |
For example, the $24 received by the Indians for Manhattan in 1626 would grow to $1.2 billion invested at 5% and to $25,454 TRILLION invested at 10%. Note that the Indians could therefore easily buy back Manhattan Island, including all its buildings, if they had invested the $24 at an interest rate between 5% and 10%. (If they had invested the $24 at 10%, they could buy everything in the entire world!)
By the way, the statement at the top is often attributed to A. Einstein, but apparently it was not said by him. Alice Calaprice, the author of The Quotable Einstein says "I have never run across it in my readings, and I don't think Einstein said it". Thanks to Steve Feldman for asking about the source of this quotation, leading to the discovery that no reference could be found for this quote.
Nonetheless, as the table and examples above make abundantly clear, compound interest is indisputedly an extremely powerful force, especially at high interest rates, and the cachet of Albert Einstein is not needed to prove that point.
Note that it is NOT true that "it takes money to make money". That is just a convenient excuse for people to spend all or more than they are earning! In fact, the OPPOSITE is true. If you have too much money, you cannot take advantage of many opportunities. For example, if you have a billion dollars to invest (as do many mutual funds, pension funds, and other billionaires), you effectively cannot invest in "small companies" (ones with a total value less than $100 million) for two reasons. First, you cannot put a significant portion of your assets into them because the total worth of the company is a small percentage of your assets. Second, if you try to buy more than a small percentage of the total stock of a small company, your large purchase or sales order would totally disrupt the market, causing the price to go heavily against you! Small investors don't have to worry about either of these effects.
WHY IS IT IMPORTANT TO SAVE?
There are at least three fundamental reasons to save.
1. Savings are important to tide one over transition periods in life. For example, if you lose your job or are between jobs, you need a several-month savings cushion to prevent drastic changes in your lifestyle.
2. Savings are necessary to best make several commonly desired purchases. Examples are a car, a house, a college education, etc.
3. Savings are critically important in maintaining your lifestyle during retirement. Social Security returns very little to workers who have been contributing throughout their lifetimes. For example, someone contributing the maximum amount of money each year into Social Security will receive a maximum benefit of about $10,000 per year in 1989 dollars. Note that the contributions came from a salary base of $48,000 per year in 1989 dollars.
The JPL/CIT retirement program is significantly better than average. NOTE: The following section is now invalid, since the Prudential plan was converted to TIAA/CREF. More about this when I have the time. The aim of the Prudential Retirement Plan is that a 25 year employee who retires at age 65 will receive 60% of their final salary, including half of their Social Security income. Thus the total benefits for such a person will be 60% of their final salary plus no more than $5,000 per year. Note that this benefit is not adjusted for inflation, so its value decreases every year.
More precisely, each year a JPL/CIT employee accrues a benefit of 2% of their final salary (since 1982; it was 1% before July 1, 1969). Thus someone working for JPL/CIT from 1984-1988, a total of 5 years, would retire with a benefit of 10% of their final salary.
For those in the TIAA/CREF plan, the employee contributes the "old age pension" part of Social Security (5.7% in 1989) of their salary in excess of the Social Security wage base ($48,000 per year in 1989), and CIT contributes 14% minus the CIT contribution to the "old age pension" (5.7% in 1989). Note that this is a defined contribution plan, not a defined benefit plan, so the final retirement benefit depends on how well TIAA/CREF does over the years. You must do your own computation to calculate your benefit. For the example given above of a 5 year employee, the total contribution would be about 9% of salary per year, which would total 45% of final salary, assuming salaries increase at about the inflation rate. This would buy a 20 year annuity of about 22% per year of final salary.
In any case, the danger inherent for any retirement income is the effect of inflation. The typical 65 year old can expect to live 20 more years. In that period, 5% inflation would reduce your real dollar retirement benefit by a factor of 2.65! If you have no savings, you have no way to offset this reduction in your income. Your 60% in final salary effectively becomes 23% of final salary after 20 years!
There is a basic test to apply if someone is trying to sell you such a scheme. Ask the following question - If what he says is true, would he be saying it to me? At low levels of return, an advisor or broker can be more successful by selling his advice for a fee or for a commission. Beyond that level of return, the salesman would be better off using that advice himself by borrowing money and following his own advice. (Note that doubling your money in a year corresponds to an interest rate of 1.00 in Table 1, way beyond the last entry in that Table, which would produce incredible wealth quickly!)
Furthermore, that advice would only work if no one else knows the advice! If anyone else found out about it, they would quickly invest their money in the same way UNTIL the level of return offered by following that advice declines to the SAME LEVEL of return offered by other investments that are equally risky. (More about this later.)
Precept number 3 implies:
- NEVER buy anything from unsolicited salesmen
- NEVER buy anything you read about in the papers or elsewhere touted as "The investment of the century" or "Double your money in only 6 months", etc.
A corollary is that if everybody's doing it, watch out! (More about this later) Examples:
- Everybody started to make incredible money from the stock market just before its crash in 1987
- Everybody started to invest in Southern California rental properties in 1977-1979, just before 5 years of depreciating real estate prices.
- Everybody started to speculate in oil just before prices crashed in 1986.
- Everybody started to buy gold just before it crashed in 1980.
These precepts are the fundamentals. Without a firm grasp of all three, there is no point in going further. For example, unless you understand the power of compound interest, you won't know why it is important to save, nor be able to carry out a sound investing plan. Without savings, there is nothing you can do. Without understanding precept number 3, you will probably not be very successful at investing, and may even lose whatever savings you do have!