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An Impassioned Plea for Understanding Compound Interest

   Posted On: June 4, 2013  |    Posted In: Personal Finance 101  |     Posted by: Broke Millennial®

I hate math. I’m not talking about a vague dislike of x+y = z, we’re dealing with full-unadulterated hatred.  Frankly, I blame second grade. My teacher, Ms. Pruitt, insisted we memorize our multiplication tables from 0 through 12. She even made us flash cards to aid the process. As an epic memorizer, I felt confident this task would be easy, but for some reason numbers made my brain want to shut down. Even at seven. Needless to say, there may have been a moment when I dramatically crumpled up a flash card and threw it on the ground in a math-induced-rage.

As my schooling progressed, math continued to be the bane of my existence. Well, I could still pull a B in the course, but I hated every second of it. As the years went by and the theories (theorems? proofs?) became more abstract or just plain dumb, in my very biased opinion. Instead of trying to understand the pages of numbers or even worse, word problems, my mind would just go on a casual stroll. Only one chapter of math briefly taught during my high school education made complete sense: finances.

I’m not sure if the typical American math curriculum includes a chapter on finances (I spent 5th – 12th grade overseas), but it seems a lot of millennials don’t understand the concept of compound interest. If you don’t understand compound interest then you’ll never get excited about saving and investing your money. Millennials need to grasp the basic fact it isn’t your salary making you rich, it’s your abilities to save your income and invest it wisely.

Every year, month and day matters when it comes to amassing your wealth and preparing for retirement, which is why it’s imperative millennials understand the importance of starting now.

I refer you to this example from JD Roth over at Get Rich Slowly:

If 20-year-old Britney makes a one-time $5,000 contribution to her Roth IRA and earns an average 8% annual return, and if she never touches the money, that $5,000 will grow to $160,000 by the time she retires at age 65. But if she waits until she’s [author’s] age (39) to make her single investment, that $5,000 would only grow to $40,000. Time is the primary ingredient to the magic that is compounding.

Sounds great (or scary), right? But you might be wondering exactly what is compound interest?

First let’s start with interest or “simple interest.” Interest can work for you or against you. In the simplest form, interest is a fee being paid by a borrower to a lender. If you put your money in the bank, the bank is then using your money (nope, it doesn’t just sit there in a vault) and paying you a small percentage to do so. Or if you borrow money, hello student loans, then you’ll owe the initial amount of your loan plus the interest you’ve accrued in the years it has taken for you to pay it off. Simple interest is only paid on the initial principal. Stay with me now, it’s about to get exciting!

Compound interest is proof of the proverb money begets money. With compound interest, your money will earn interest on the interest already accumulated. Let’s break it down.

You invest $4,000 using simple interest for 2 years with an interest rate of 8%. At the end of the first year you’ll have earned $4,320. At the end of the second year you’ll see $4,640 in your account.

Now, take the same investment and use compound interest. The first year, you’ll earn the same amount you would using simple interest, $4,000 x 8% = 320. However, in the second year instead of just accruing interest on the original $4,000 you’ll get to use $4,320.  The formula will then be $4,320 x 8% instead of $4,000 x 8%. At the end of your second year you’ll have amassed $4,665. Doesn’t sound like much now, but what if we expand the example to five years?

With simple interest you can use a quick, one-time formula: $4,000 x .08 x 5 = $1,600.  You’ll have a total of $5,600.

For compound interest, I’ll show you the growth each year. We already know you’ll have $4,665 by the end of your second year, so let’s compound it for the next three.

Year 3: $4665 x .08 = 373.2 [5,038.2]
Year 4: $5,038.2 x .08 = 403.1 [5441.26]
Year 5: $5,441.26 x .08 = 435.3 [$5876.56]

You were investing the same principle amount and over the same period of time, but with compound interest earned $276.56 more than you would using simple interest. There is even a simple way to quickly discover the length of time until your money doubles, the rule of 72. Using this dreaded math theory (theorem? proof?) you simply divide 72 by your interest rate. In our example above it would take 9 years to double the principle investment.

My point? Make sure you’re taking advantage of compound interest. Namely, open up a Roth IRA and/or make sure to take advantage of your company’s 401(k). The longer you procrastinate the more money you’re throwing away. I mentioned last week too many of my peers keep making excuses about deferring planning for retirement. Don’t make excuses and just figure out how to make it work. You won’t regret it.

Even the Wall Street Journal agrees: It’s Never Too Soon to Start Planning Your Retirement.


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34 responses to “An Impassioned Plea for Understanding Compound Interest

    1. Thanks, Michael! I tried to break it down best I could because a lot of sites and books are really vague and frankly I have trouble understanding what they mean.

      And you’re so right. Plenty of people just sit on their money without having it work for them or blindly invest.

  1. “It isn’t your salary making you rich, it’s your abilities to save your income and invest it wisely.” Truer words have never been spoken. Great overview of such a basic but important concept. Probably my favorite quote on this topic comes from Benjamin Franklin: “Money makes money. And the money that money makes makes more money.”

  2. Hate math, love compound interest! I didn’t realize how much I was “losing” by not investing sooner. I recently (after I finally paid off my student loan debt) started investing in a 403b. Not a lot of money, but anything is better than nothing and I’m counting on that compound interest to help me out.

  3. Retirement savings is difficult for millenials because we have a hard time envisioning 5 years from now, let alone 40+ years from now. I think auto-deductions from your checking or savings account each month to a Roth or an auto-deduction from your paycheck to a 401k is an excellent way to get started saving for retirement. It’s a bit depressing to think how much we need for retirement, or looking at all the risks behind our fiat dollar currency, but getting dollars in the bank is the first step. If you want to diversify further into international stocks, gold, etc. that really can’t be done until you have money in your retirement account. Sorry I seriously digressed from compound interest, but my mind wanders when we start talking about these topics 😉

  4. “Millennials need to grasp the basic fact it isn’t your salary making you rich, it’s your abilities to save your income and invest it wisely.” Great post! He had an IRA account when we got married, smart man 🙂 Need to look at possibly adding a bit more $$ to it because I know we took some out before. Thanks for writing on this!

  5. Wonderful post, Erin! I have a lot of clients who are shocked to realize what they lost by waiting to start investing. They thought they needed a lot of money to start investing. Putting a few dollars away a paycheck may not seem like much, but it does grow. And it is FUN to make rain with fake or real money! 🙂

  6. Great job! You explained it so well! I actually understand it and it makes me want to start saving asap! But I don’t have 401k option with work… I haven’t been here long enough and basically don’t meet the company’s qualifications (yet). What do you suggest I do?

  7. The earlier you can start, the better. I also think that if a person starting out automatically starts putting a certain percentage in investments, they won’t have to adjust to not having money saving later because they will already be used to not having it.

  8. Math induced rage. Haha, im always astounded when my friends tell me it’s not worth investing their money now. Retirement is so far away they say. But even if you don’t want to retire early, just max out your ira 5 or 6 years in a row in your 20s, then you’ll never have to worry about your retirement.

  9. This is a GREAT explanation! Thank you for taking the time to write it. It took me longer than I would have liked to realize that I was throwing money away by not investing in my retirement.

  10. Triple yay! Love compound interest. Love Roth IRAs. Love starting early. If you have teens who had a summer job last year or any W-2 wages, do them a favor: open up a Roth IRA for them and giving them some parental matching on any contributions they make. Dan Kadlec over at TIME Money calls that a “Family 401(k)” and it’s my favorite family finance tip of all time. If you want to teach young kids the concept of compound interest in an accelerated fashion and with amounts that will get their attention (neither of which you’ll find in any real savings account), give them a crazy awesome Bank of Mom/Dad interest rate that compounds weekly and is paid/calculated by you. They just might form a lifelong savings habit that way by the age of 7 or so which is when some experts claim money habits are formed (yikes!).

  11. Many years ago when we were saving for our son’s college education, I took him with me to the bank to take out a CD for his college fund. While there, I explained to him that by putting money in that account, the bank would give us “free” money at the end of the year. And then at the end of the 2nd year, the bank would give us free money for the money they gave us the first year. His eyes got wide and he said “so they’ll give us money on top of the money they gave us first?” He was so impressed he started bringing me money from his allowance and chores payments to put in the bank to earn interest. I think I helped him start a life-long habit with that one visit to the bank.

  12. I can just smell my ROTH IRA baking in the oven. This is a super awesome post that I can’t wait to share with some of my good friends curious about investing.

  13. Why is it that every financial post uses high interest rates of 8% or more in examples of how money can grow over time? This in surely not the case for most people. The markets avg. is below 8% and has been for a while.

    1. Hi Leo – Often you’ll actually read 11% – 12% returns because people speaking about compound interest are usually making the point over a 30 to 40 year span. 8% is the conservative number for the market over a long duration of time and not just a few years.

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