Compound Interest

In your efforts to appreciate the potential of your $10,000 to multiply itself, you have acquainted yourself with two of the most important concepts in finance. As we’ve already indicated, one is the principle of compound interestInterest earned on your savings is added to the money in your savings account, and the new total (principle plus interest) earns more interest., which refers to the effect of earning interest on your interest.

Let’s say, for example, that you take your grandfather’s advice and invest your $10,000 (your principal) in a savings account at an annual interest rate of 5 percent. Over the course of the first year, your investment will earn $512 in interest and grow to $10,512. If you now reinvest the entire $10,512 at the same 5 percent annual rate, you’ll earn another $537 in interest, giving you a total investment at the end of year 2 of $11,049. And so forth. And that’s how you can end up with $104,345 at age sixty-five.

Time Value of Money

You’ve also encountered the principle of the time value of moneyThe principle whereby a dollar received in the present is worth more than a dollar received in the future.—the principle whereby a dollar received in the present is worth more than a dollar received in the future. If there’s one thing that we’ve stressed throughout this chapter so far, it’s the fact that, for better or for worse, most people prefer to consume now rather than in the future. This is true for both borrowers and lenders. If you borrow money from me, it’s because you can’t otherwise buy something that you want at the present time. If I lend it to you, it’s because I’m willing to postpone the opportunity to purchase something I want at the present time—perhaps a risk-free, ten-year U.S. Treasury bond with a present yield rate of 3 percent.

I’m willing to forego my opportunity, however, only if I can get some compensation for its loss, and that’s why I’m going to charge you interest. And you’re going to pay the interest because you need the money to buy what you want to buy. How much interest should we agree on? In theory, it could be just enough to cover the cost of my lost opportunity, but there are, of course, other factors. Inflation, for example, will have eroded the value of my money by the time I get it back from you. In addition, while I would be taking no risk in loaning money to the U.S. government (as I would be doing if I bought that Treasury bond), I am taking a risk in loaning it to you. Our agreed-on rate will reflect such factors.See Timothy J. Gallager and Joseph D. Andrews Jr., Financial Management: Principles and Practice, 3rd ed. (Upper Saddle River, NJ: Prentice Hall, 2003), 34, 196.

Finally, the time value of money principle also states that a dollar received today starts earning interest sooner than one received tomorrow. Let’s say, for example, that you receive $2,000 in cash gifts when you graduate from college. At age twenty-three, with your college degree in hand, you get a decent job and don’t have an immediate need for that $2,000. So you put it into an account that pays 10 percent compounded and you add another $2,000 ($167 per month) to your account every year for the next eleven years.This 10 percent interest rate is not realistic for today’s economic environment. It’s used for illustrative purposes only. The left panel of Table 14.3 "Why to Start Saving Early (I)" shows how much your account will earn each year and how much money you’ll have at certain ages between twenty-three and sixty-seven. As you can see, you’d have nearly $52,000 at age thirty-six and a little more than $196,000 at age fifty; at age sixty-seven, you’d be just a bit short of $1 million. The right panel of the same table shows what you’d have if you hadn’t started saving $2,000 a year until you were age thirty-six. As you can also see, you’d have a respectable sum at age sixty-seven—but less than half of what you would have accumulated by starting at age twenty-three. More important, even to accumulate that much, you’d have to add $2,000 per year for a total of thirty-two years, not just twelve.

Here’s another way of looking at the same principle. Suppose that you’re twenty years old, don’t have $2,000, and don’t want to attend college full-time. You are, however, a hard worker and a conscientious saver, and one of your (very general) financial goals is to accumulate a $1 million retirement nest egg. As a matter of fact, if you can put $33 a month into an account that pays 12 percent interest compounded,This 12 percent rate is unrealistic in today’s economic environment. It’s used for illustrative purposes only. you can have your $1 million by age sixty-seven. That is, if you start at age twenty. As you can see from Table 14.4 "Why to Start Saving Early (II)", if you wait until you’re twenty-one to start saving, you’ll need $37 a month. If you wait until you’re thirty, you’ll have to save $109 a month, and if you procrastinate until you’re forty, the ante goes up to $366 a month.See Arthur J. Keown, Personal Finance: Turning Money into Wealth, 4th ed. (Upper Saddle River, NJ: Pearson Education, 2007), 23.

The moral here should be fairly obvious: a dollar saved today not only starts earning interest sooner than one saved tomorrow (or ten years from now) but also can ultimately earn a lot more money in the long run. Starting early means in your twenties—early in stage 1 of your financial life cycle. As one well-known financial advisor puts it, “If you’re in your 20s and you haven’t yet learned how to delay gratification, your life is likely to be a constant financial struggle.”Jonathan Clements, quoted in “An Interview with Jonathan Clements—Part 2,” All Financial Matters, February 10, 2006, http://allfinancialmatters.com/2006/02/10/an-interview-with-jonathan-clements-part-2/ (accessed November 11, 2011).