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Smart FI Sprint Podcast EP 002: The Magic of Compounding Interest

in Interest, Investing, Podcast

Another podcast in the beginning series regarding the basics of Financial Independence! We all need to know about compounding interest because it controls our financial lives. It allows us to see what that new loan really costs us. How our investments can grow overtime, and the cost benefit analysis of buying something new vs. investing that money instead!


Smart FI Sprint Podcast EP 002: Abra Kadabra, The Magic of Compounding Interest


  1. Update
    1. Redesigned front page/website!
      1. I feel pretty proud of it because I’ve been doing everything for myself!
      2. Learning to code in HTML and CSS
  • However, I haven’t mastered responsive web design in a lot of ways yet, so the website can look fruity on tablets and mobile phones. I apologize for that, and will be working vigorously in the future to try and correct the problem J
  1. Going to get a logo made soon
  2. Update on writing/books
    1. Delirium
      1. Rough draft finished, now working on first edit
      2. Hopefully have it done by the summer season at some point
    2. College Personal Finance
      1. I believe I have a wealth of experience from college that I have reflected on and can share with future and current students, as well as parents of current and future students. Hopefully it will be as helpful as I think it will be!
    3. Other goings-on in my life
      1. Going to be 26 in less than a month, so I have to get on my own insurance
        1. Another $600/year for myself for health insurance
      2. Getting married in 3 months
    4. Got my first ever profit sharing bonus
      1. Watching that 401k grow!
      2. Officially have over $5k in investments now
    5. Compounding Interest
      1. Defined as – interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.
        1. Basically, you can think of it as interest on interest
        2. Compounding interest makes your investment or debt grow faster than normal/simple interest
          1. Simple interest only accrues on the normal principle amount
        3. The math
          1. Something we should probably care about when it comes to compounding interest is future value
            1. Future value is found by multiplying the present value times one plus nominal interest rate over compounding frequency to the power of the compounding frequency times time
            2. Or, in algebraic terms,
              1. n = compounding frequency, ex. If compounded monthly, then over a year would be 12, or two years would be 24
              2. t = time, could be in years (1 year, .5 years (6 months), etc.)
              3. I = nominal interest rate
            3. This simple formula can tell you how much money you would make on something like a bond, and it can tell you how much money you would end up owing on something like a student loan
            4. We can then use the future value and the present value to find out what the compound interest paid would be
              1. CI = F – P
            5. But Don, I don’t want to do all of this math to figure out how much money I could have every time! That’s a lot. Well, have I got the perfect solution for you! It is the continuously compounding interest formula
                1. Where P is the present value, e is the exponential, r is the (interest) rate and t is the period of time, e.g. 12 months, 1 year, etc.
              1. Basically, you just push your compounding frequency to infinity.
              2. I know, this sounds like it doesn’t make any sense, and in some sense, it isn’t realistic
                1. Your money won’t be compounded in infinitesimally small amounts. It’s compounded on a more normal basis, e.g. every 12 months, 6 months, 1 month, every day, etc.
              3. However, it is a useful model because it gives a very good estimate of the future value of something without the more complex math or the compounding increments
  • Let’s do an example to show how well the continuously compounding formula works
    1. Let’s say you are thinking about getting a brand new car (cough*TERRIBLE IDEA*cough).
      1. You think you’re being reasonable with getting a new car for 23k. Now let’s say you put down 3k and you take a 5 year loan out at 6.4% interest for the remaining 20k.
        1. Hold up, now, let’s add on the money for sales tax, $1610 (or 7% in Indiana). That puts you at about 25k total with a 22k remaining
      2. To find out how much you’ll really be paying for that car, let’s use the continuously compounding interest formula
      3. Present value of the loan is 22,000. The time to repay is 5 years and your rate is .064
      4. Plug it all in and you get a grand total of $30,296.80! For that car, you’ll be paying over $8k extra!
        1. That’s pretty insane. All because you borrowed someone else’s money
        2. Near the end of the show, I’ll really put this into terms you can be amazed about with a cost-benefit analysis
      5. Brief Overview of Investment Vehicles w/ Compound Interest
        1. I just want to give a quick run through of a couple well known financial instruments with compounding interest. I’m sure you know a couple of these, if you are not very well acquainted with them.
        2. Bonds
          1. Bonds are one of the primary investment vehicles in financial markets for the typical individual.
          2. The money you earn from them is based on interest rates
          3. Right now, bonds are kind of a lousy investment since interest rates are so low
            1. But on the bright side, they will get better as interest rates increase in the future
  • CDs
    1. Also known as Certificates of Deposit
    2. CDs are issued by banks, and once invested in a CD, you cannot withdraw money from it (unless you want to face a penalty) until the time is up
    3. The unlike stocks, the interest rate of a CD is fixed, but unlike a bond, you cannot sell your CD
  1. Stocks
    1. Along with bonds, stocks are the second primary investment vehicle for the typical individual
    2. Although stocks do not earn compound interest in the normal sense (they are not interest bearing vehicles), you can reinvest dividends which will then compound in addition to appreciation of your stock. This compounding leads to (in theory), infinite growth since things just keep snowballing on each other.
  2. Debt Vehicles w/ Compound Interest
    1. Mortgage
    2. Student Loans
      1. Government
      2. Private
        1. My private loans compound interest daily. It is a raw deal because each day I see that interest going up. Never fun.
  • Credit Card Debt
    1. Compounds at an insane rate, typically with insanely high interest rates. That’s why you always, always, always try your hardest to completely pay off credit card debt before the due date. Only bad things can happen when you carry a credit card balance.
  1. All of these loan types accrue interest continuously. This means I can go in and look at my private student loan on day one. It will have, let’s say $4.56 of interest, and the next day, it will have $9.
  2. This is why paying things off on time, and if possible, faster, can really save you a toooon of money in the long run
  1. Cost-Benefit Analysis
    1. Finally, continuously compounding interest is great for performing a cost benefit analysis!
    2. I actually want to show a couple of examples, but starting with the previous one…
      1. You look and say, “Don, Learning Guy. I’m going to be honest. I don’t know if I really want that shiny new car anymore.”
      2. Then I say, “Congrats! You’re stepping in the right direction. Now, let me show you an even greater reason not to get that shiny new car (and shiny new loan).”
      3. Let’s say you’re able to find an economical, sporty, used 2009 Honda Fit for $7800 and you make a one-time payment for it. This allows you to save about $22.5k.
        1. “Wow…you might be on to something,” you mumble, but wait! There is more.
      4. If you were to invest that money instead over 5 years, and get the average annual return of the stock market, which is 7%, you would end up with almost $32k instead!
      5. Think about that. You’d have a fuel-efficient, economical, good-looking vehicle in addition to have $32k saved
      6. How about if we project that out over 10 years?
        1. Boom, now you have $45.5k
      7. How about 20 years?
        1. $91.5k. That’s right. Your 25k turns into nearly 100k after 20 years
  • Now we shall do one example of DEBT
    1. You have just graduated college and have a private loan for $18k with a 8% interest rate. You decide you only need to pay the minimum every month, let’s say $231.55, meaning it will take 10 years to repay the loan.
    2. The interest compounds daily, but for the sake of expediency and ease, we will once again use the continuous compounding interest formula.
    3. Over 10 years, that $18k loan will balloon into $40,059.70.
      1. That is an extra $30k for paying the minimum on your loan over ten years.
    4. This is the power of compounding interest. For better or worse. Pretty amazing, huh?

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