## Get time on your side

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### The time value of money (TVM)

Why do you expect to receive interest on money you lend (and to pay interest on money you borrow)? Partly it’s to compensate you for the risk that money you lend might not be repaid, or that inflation might have eroded its value before it’s repaid. But there’s an even more fundamental reason that applies even to risk-free investments. A dollar that is yours to use today is more valuable than a dollar you won’t get until some time in the future. Interest payments compensate you for giving up the use of your money today.

The future value of money is the value to which it would grow over time at a particular rate of interest. The future value of a dollar next year at 5% is \$1.05. The present value of money is the value today of an amount to be received in the future. If the ratio of future value to present value is 1.05, then the present value of a future dollar is 95.2 cents (1 / 1.05 = .952).

The time value of money becomes much more obvious over longer time periods. Then the growth over time is based on compound interest. At 5% interest compounded, the future value of a dollar after 20 years is \$2.65, while the present value of a dollar you won’t receive for 20 years is only 38 cents. Future value is calculated by compounding present value, and present value is calculated by discounting future value. The calculations can be done easily on a business calculator or a spreadsheet using mathematical functions.

The financial significance of time depends on whether you are in a vicious circle of debt or a virtuous circle of saving, as described in the previous post. When you borrow, time works against you because of the accumulation of finance charges. When you save and invest, time works for you because of the compounding of earnings. The future value you receive is your reward for sacrificing present value. Appreciate the power of compounding, and get it working for you instead of against you.

### Doubling time

An easy way to demonstrate the power of compounding is to calculate the “doubling time,” how long it takes an investment to double at a given rate of return. Suppose you invest in the stock market and earn 10% a year (which is close to the historical norm). On the average, about 3% of that will represent inflation, so let’s say that the real return is about 7%. Anything that grows at 7% doubles in about 10 years. (You can calculate an approximate doubling time for anything by dividing the annual rate of growth into 72.) And that means it quadruples in 20 years and grows by a factor of about eight in 30 years. That’s the benefit of long-term investing, which you miss out on by not getting started as early as you can. Procrastinate for 10 years, and you can miss one whole doubling.

At 7% per year, \$1000 invested at age 35 will grow to \$7,612 by age 65, but the same amount invested at age 25 will grow to \$14,974 by age 65. And \$1000 invested every year from 35 to 65 will grow to \$94,461, but the same amount invested every year from 25 to 65 will grow to \$199,635.

### Long-term implications of savings rates

Let’s use TVM to tackle a more difficult problem, the relationship between a household’s savings rate during the working years and its income during the retirement years.

The Census Bureau classifies households by age, based on the age of the “householder,” the adult who is listed first on the reporting form. For this simplified example, let’s assume that households with householders 25-64 are in the working years, and those with householders 65-94 are in the retirement years. So forty years of working and saving might have to support thirty years of retirement. Let’s also assume that within each five-year age group from 25-29 to 60-64, a household receives the median household income for its age group, and invests a portion of it in a diversified portfolio earning a 5% real return after inflation.

Let’s compare the average income before retirement to the average income after retirement, for households with various savings rates. For the average income before retirement, we’ll use the same figure for all households, the average income over all the age groups 25-64. To get a post-retirement income, we can calculate the nest egg a household would accumulate by age 65 with a given rate of savings. We will then make the conservative assumption that they could withdraw at least 4% of that nest egg in each year of retirement. (Withdrawal rates will be discussed in a later post.)

Now we can calculate a “replacement percentage,” the percentage of the average pre-retirement income that would be replaced by the post-retirement income. With these assumptions, the replacement rate comes out about five times the savings rate. If the household saved 5% of its income consistently during its working years, it could have a post-retirement income equal to 25% of its average pre-retirement income. If it saved 10%, it could replace 50%; and if it saved 15%, it could replace 75%. Most households needn’t plan on trying to replace all of their income with earnings on savings, because they should have additional sources of retirement income, such as Social Security, part-time earnings, or a pension. They may also have reduced expenditures, as a result of downsizing or paying off the mortgage.

### More sophisticated projections

Projections like this are useful for appreciating the importance of the savings rate, but they are too general to predict the future incomes of particular households. With today’s computers, financial advisors can do far more sophisticated projections, which take into account more factors. They can take into account variations in asset allocation, such as how much of the household’s investments are in the stock market. They can take into account different rates of taxation for different investments, as well as differences in tax brackets for different taxpayers. They can take into account the ups and downs of markets and the timing of the ups and downs. You could have a very bad bear market just when your savings are at their peak. Sophisticated financial planning software can do “Monte Carlo” projections, which summarize the results of thousands of scenarios and calculate the probability of achieving a financial goal. No projection, no matter how sophisticated, can guarantee any one future, but we can identify futures that are more likely than others, based on historical experience.

### Time and uncertainty

The idea of getting time on our side is not without its limitations. Once we start considering long time frames, such as the life of a human being, historical change becomes a factor. Fundamental assumptions of our financial models, such as average rate of return and normal variations in return, may turn out to have been features of a particular historical era. If you plan to live in your house for fifty years, it better be able to withstand a fifty-year storm. But what if storms that used to occur only once in a hundred years start occurring about every ten years, as a result of global climate change? Or on the financial front, what if economic globalization makes markets more volatile and economic depressions more frequent? No set of investing principles can guarantee economic security in an uncertain world. But principles that have “stood the test of time” at least up until now are better than no principles at all.

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