Personal Finances

Learning Objectives

1. Explain compound interest and the time value of money.
2. Discuss the value of getting an early start on your plans for saving.

The fact that you have to choose a career at an early stage in your financial life cycle isn't the only reason that you need to start early on your financial planning. Let's assume, for instance, that it's your eighteenth birthday and that on this day you take possession of $10,000 that your grandparents put in trust for you. You could, of course, spend it; in particular, it would probably cover the cost of flight training for a private pilot's license - something you've always wanted but were convinced that you couldn't afford for another ten or fifteen years. Your grandfather, of course, suggests that you put it into some kind of savings account. If you just wait until you finish college, he says, and if you can find a savings plan that pays 5 percent interest, you'll have the $10,000 plus another $2,209 to buy a pretty good used car.

The total amount you'll have - $12,209 - piques your interest. If that $10,000 could turn itself into $12,209 after sitting around for four years, what would it be worth if you actually held on to it until you did retire - say, at age sixty-five? A quick trip to the Internet to find a compound-interest calculator informs you that, forty-seven years later, your $10,000 will have grown to $104,345 (assuming a 5 percent interest rate). That's not really enough to retire on, but after all, you'd at least have some cash, even if you hadn't saved another dime for nearly half a century. On the other hand, what if that four years in college had paid off the way you planned, so that (once you get a good job) you're able to add, say, another $10,000 to your retirement savings account every year until age sixty-five? At that rate, you'll have amassed a nice little nest egg of slightly more than $1.6 million.

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 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 money - 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.

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.

Table 14.3 Why to Start Saving Early (I)

	Savings accumulated from age 23, with deposits of $2,000 annually until age 67			Savings accumulated from age 36, with deposits of $2,000 annually until age 67
Age	Annual deposit	Annual interest earned	Total saved at the end of the year	Annual deposit	Annual interest earned	Total saved at the end of the year
23	$0.00	$0.00	$0.00	$0.00	$0.00	$0.00
24	$2,000	$200.00	$2,200	$0.00	$0.00	$0.00
25	$2,000	$420.00	$4,620	$0.00	$0.00	$0.00
30	$2,000	$1,897.43	$20,871.78	$0.00	$0.00	$0.00
35	$2,000	$4,276.86	$47,045.42	$0.00	$0.00	$0.00
36	$0.00	$4,704.54	$51,749.97	$2,000	$200.00	$2,200.00
40	$0.00	$6,887.92	$75,767.13	$2,000	$1,221.02	$13,431.22
45	$0.00	$11,093.06	$122,023.71	$2,000	$3,187.48	$35,062.33
50	$0.00	$17,865.49	$196,520.41	$2,000	$6,354.50	$69,899.46
55	$0.00	$28,772.55	$316,498.09	$2,000	$11,455.00	$126,005.00
60	$0.00	$46,338.49	$509,723.34	$2,000	$19,669.41	$216,363.53
65	$0.00	$74,628.59	$820,914.53	$2,000	$32,898.80	$361,886.65
67	$0.00	$90,300.60	$993,306.53	$2,000	$40,277.55	$442,503.09

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.

First Payment When You Turn	Required Monthly Payment	First Payment When You Turn	Required Monthly Payment
20	$33	30	$109
21	$37	31	$123
22	$42	32	$138
23	$47	33	$156
24	$53	34	$176
25	$60	35	$199
26	$67	40	$366
27	$76	50	$1,319
28	$85	60	$6,253
29	$96

Key Takeaways

• The principle of compound interest refers to the effect of earning interest on your interest.
• The principle of the time value of money is the principle whereby a dollar received in the present is worth more than a dollar received in the future.
• The principle of the time value of money also states that a dollar received today starts earning interest sooner than one received tomorrow.
• Together, these two principles give a significant financial advantage to individuals who begin saving early during the financial-planning life cycle.

Exercise

(AACSB) Analysis

Everyone wants to be a millionaire (except those who are already billionaires). To find out how old you'll be when you become a millionaire, go to http://www.youngmoney.com/calculators/savings_calculators/millionaire_calculator and input these assumptions:

Age: your actual age

Amount currently invested: $10,000

Expected rate of return (interest rate): 5 percent

Millionaire target age: 65

Savings per month: $500

Expected inflation rate: 3 percent

Click "calculate" and you'll learn when you'll become a millionaire (given the previous assumptions).

Now, let's change things. We'll go through this process three times. Change only the items described. Keep all other assumptions the same as those listed previously.

1. Change the interest rate to 3 percent and then to 6 percent.
2. Change the savings amount to $200 and then to $800.
3. Change your age from "your age" to "your age plus 5" and then to "your age minus 5".

Write a brief report describing the sensitivity of becoming a millionaire, based on changing interest rates, monthly savings amount, and age at which you begin to invest.