compound interest

How to Save $1 Million

July 13, 2016 By Jennifer Clark 1 Comment

Being able to save $1 million dollars may seem completely unattainable and ambitious, especially if you are knee deep in debt. But the fact of the matter is, with some wise investments and choices, you can get there in due time.

How can this be? Two words: compound interest. Compound interest is, in simple terms, interest that is building upon your interest. When you use a savings or investment platform such as a retirement fund or 401 (k), you have the opportunity to gain additional interest to your funds.

As the principal gains interest, your gain plus the original principal amount gain interest. The more it is compounded, the continuous the growth of interest is.

Saving $1 Million is a Science

To find out how much you will make from compound interest, there is a formula you can use:

V=P(1+r/n)^nt
- Broken down, each part of the formula is:
  - V=the value of the investment after the compounded interest
  - P=principal investment amount
  - r=annual interest rate
  - n=number of times interest is compounded yearly
  - t=the number of years the money is invested

If this still seems a bit confusing for you, you can head over to The Calculator Site and use their automatic compound interest calculator to determine your total amount.

If you see a formula that is V=P(1+r)^t, this is a simplified version of the formula assuming interest is compounded once per year or per period instead of monthly or multiple times per period.

Let’s use this formula ourselves to see how long it will take to save $1 million.

Using the Formula to Save $1 Million

If we assume that you are contributing to a retirement fund with a 5% compound interest rate, and we base our formula on annually rather than multiple times per year, we will need to use the Internal Revenue Service’s 2016 annual contribution limit of $18,000.

Moving forward, here is what it would look like:

V=$18,000(1+ 0.05)^1
V=$18,009

This may not seem like a lot, but the longer the money hangs in the account, the more you make (as long as you keep investing). It is helpful to keep adding money every year as well. So, let’s try increasing it by several years with a continued annual contribution of $18,000 using the updated formula below and see what happens.

V=$18,000(1+0.05)^26+$18,000 ((1+0.05)^(1+26)-(1+0.05))/0.05
V=$1,030,046.38

As you can see, with the amounts and rates provided, it would take you 26 years to hit $1 million, assuming this would be a 401 (k) with a match plan. Without the additional contributions, it would take roughly more than 82 years to reach that point.

When exploring options for investment funds like this, you will want to not only consider the compounding interest but also the rate, the compounding period or frequency and annual contribution. These factors will help your investments go farther. What route you choose depends on how quickly you are hoping to grow your wealth.

For instance, if you have one penny that you doubled every year you would have approximately $5.3 million in 30 years. If you doubled it every day, you would have that same rough amount of $5.3 million in one month. While the total is the same, you can see the significant difference in frequency.

By starting your investments today, you can work your way to save $1 million sooner rather than later through patience, diligence and smart choices.

Do you currently invest? Are you benefiting from compound interest?

Photo: Flickr: Keith Cooper

Be Young, Be Frugal

February 24, 2012 By Jennifer Derrick 6 Comments

I was pretty young when I got serious about saving money and being more frugal. I didn’t do it with some grand notion of preparing for my old age or anything, I just wanted more money for emergencies and to give me more choices in terms of where I might live and work. Looking back, though, I understand now why starting young was the smartest thing I could do.

Too many people put off saving, thinking, “I’ll save when I’m making more money, or when the kids are gone, or when I’m older and I’ve had all my fun.” The problem is that saving when you’re older becomes a dicier proposition as the years go by. Yes, you may be making more money but you’ll also likely have more demands on your money. You may get sick and become unable to work. Or, you may have to start paying people to do the things you used to do. Saving when you’re young gives you a cash reserve that you can draw on as you age and, thanks to compounding, means that you don’t have to save as much as you get older to reach your target. Here are the top reasons to save while you’re young and not put it off until “someday.”

Compound Interest

This is the most obvious reason to save while you’re young. When you save in interest-bearing accounts, your interest compounds the longer you leave the money in there. If you put ten dollars into an account earning three percent interest per month, you’ll have $10.30 at months’ end. The next month, you’ll have earned thirty-one cents in interest, bringing your total to $10.61. Even if you don’t add to the account, you continue to make money every month. The more months and years you save money and leave it alone, the more interest you will earn. Obviously this example won’t amount to much but if you’re dealing with thousands of dollars, an extra year’s or five year’s worth of interest will add up. The younger you are when you start to save, the more time your money has to grow.

As You Get Older, Things Become Harder To Do On Your Own

In your twenties and thirties, it’s nothing for you to mow your own grass, refinish your own floors, keep a garden, or paint your own house. You can save thousands by doing many chores yourself if you’re frugal. When you get older, it gets harder to do those things yourself. You may want to be frugal, but it just isn’t possible. Aches and pains may make installing a new floor impossible. Arthritic hands may mean that you can’t clutch a paintbrush for hours. You don’t even have to be elderly for these things to happen. As early as your forties you may begin to feel aches and pains that make routine chores uncomfortable. When it happens, you end up paying someone to do these things for you which will eat into any money that you’re able to save. If you’ve always thought, “I’ll save when I’m older,” you may instead find yourself paying more to have more things done for you.

Money Gets Tighter As You Get Older

If you’re fortunate your income will go up as you get older. Unfortunately, the demands on your money are likely to go up, too. You might have kids and college expenses, aging parents that require assistance, increasing healthcare expenses (even if you have great insurance), and you might want things like a bigger house or a nicer car. All of these demands on your money will eat into what you can save. You might have a big income but find your savings rate going down instead of up. If you’re also now trying to save aggressively for retirement, you might find that the money just isn’t there.

Things Get More Unpredictable As You Age

While the unexpected can happen when you’re young, it seems to happen more often as you age, simply because you have more in your life that can go wrong. Kids can get sick. A spouse can get into an accident. You can lose your job and then a month later your spouse can lose hers. You have to go back to school before you can get a new job. You can have an illness or that family history of heart disease catches up with you sooner than you planned. I don’t say this to be all doom and gloom, but the fact is that these types of accidents, injuries, and illnesses can put a serious strain on your finances. It may mean that, not only can you not continue to save, you have to dig into money you’ve already saved. You may be making a great salary but find that none of it can go into savings. If you save more when you’re young and you only have to think about yourself, you can find yourself in a better position to weather the unpredictability of later life.

Your Responses To Unpredictability Are More Limited

If you lose a job when you’re young and unencumbered, you can move more easily or take more risks to find new work. You can also cut your spending drastically, since you only have to care for yourself. When you’re older with a house and kids in school, it’s not as easy to up and move for a better job or more prospects, or to cut your spending to the bone. Unemployment insurance might be enough to see you through when you’re young whereas when you’re older with a family to support and maybe higher medical costs, it won’t be enough. If you get sick or have an accident when you’re young, you might be able to get by on Social Security or move in with family or friends to decrease your expenses. When you’re older, those responses aren’t practical or helpful. You need more money saved when you’re older to handle life’s curveballs because your other responses are going to be limited. If you saved when you were young, you’ll have it. If not, life could get a lot harder.

It’s best to put as much money away as you can when you’re young so it will be there if you need it. If you can keep saving as you age, great, but if you can’t at least you’ll have that cushion you amassed in your younger years to fall back on.

(Photo courtesy of alamosbasement)

Compound Interest – Personal Finance Fundamentals

September 7, 2008 By Jordan Lugar 27 Comments

I grew up hearing my dad say “Most people don’t know how money works.” He is a Certified Financial Planner, and while there were a few drawbacks growing up the son of a financial planner (no Gameboy or frivolous purchases unless we had saved up for them in advance), it also had huge advantages. Hearing that rich people knew something about how money worked that normal people didn’t know was naturally intriguing to me as a youth.

One of the first lessons I learned was what my dad referred to as “the miracle of compound interest.” With compound interest, opposed to simple interest, you earn interest not only on the initial investment (principal), but on the principal plus interest received to date. Because the principal balance increases with each interest payment received, the amount of interest earned each period also increases.. The longer the money is left in the investment to grow, the greater the value of the return each year.

Well, that sounds nice, but isn’t the point of investing to make money? Didn’t we all anticipate the savings to grow? Can you think of anyone who would intentionally invest their money to lose it? To help illustrate the power of compound interest, my dad gave me an example where a college student at age 20 invested $2,000 at a 6% average rate of return and never touched the money until retirement. He told me that at age 68, the account balance would be $32,000. As my financial knowledge was still in its infancy when I heard this lesson for the first time, I found it exciting that the initial investment of $2,000 could grow by $30,000 over time. I didn’t know how to calculate percent change, but it wasn’t necessary to know this was a 1,500% increase in order to recognize the significance of the growth.

In the next part of the lesson, my dad asked me what I thought would happen to the ending balance if we doubled the interest rate in the example to 12% and left everything else unchanged. I thought to myself, “what an easy question — if the interest rate doubles, the ending balance will double,” and answered that the ending balance would be $64,000. He told me that this was a good guess and that was what most people would guess, or they might add a little extra for the compounding. However, he said that most people never knew how much extra to add to the $64,000 to account for the compounding. He said that rarely had anyone ever guessed that the ending balance would be over $100,000. I thought it was preposterous that he even mentioned the six-figure number; this had to be way too high.

At this point, my dad taught me a simple formula in finance known as The Rule of 72. This formula is used to determine how long it will take for an investment to double at a given interest rate. The formula works by dividing 72 by the rate of return (72/Rate of Return % = Number of years to double). Using this formula, I realized that doubling the interest rate will not double the initial investment, but will cut the time it takes for the investment to double in half.

Returning to the question he had posed, I was astonished to find that the ending balance was not only greater than $100,000, or even $200,000, but was over a half a million dollars. I just couldn’t believe it; an investment could grow from $2,000 to over $500,000. It’s not like we were talking about letting the investment grow for eternity; on the contrary, I could experience this financial growth in my lifetime.

What this lesson teaches is that to fully maximize the potential returns from compound interest, we need to

1) start saving as early as possible to allow there to be more time for the interest to work its magic and

2) strive to obtain as great a rate of return as possible within our risk tolerance levels.

Compound interest is truly miraculous. Going back to our example one final time, given an additional 6 years at the 12% interest rate, the balance of the account would be worth over one million dollars. There is no question why Albert Einstein called compound interest “the eighth wonder of the world.”

Image courtesy of orangeacid