Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn't … pays it.
― Albert Einstein
What's the real headline here?
"Theoretical physicist says that if you don't understand compound interest, you will go broke faster than the speed of light."
This is the first post in a non-sequential series that I'm calling Math of Interest, where we will look the impacts of compounding interest in personal finance. Interest is like a river current, and you can paddle with it or against it. Do you want the flow of interest to accelerate you toward your goal, or impede your progress?
Quick lesson:
Interest is a fee charged on borrowed money. Interest and other lender fees are what incentivize financial institutions and other investors (like you) to lend money. Think of it as the cost of borrowing money and the incentive for lending money.
Compounding interest is an interest calculation method in which interest is applied to the total of principal (amount borrowed) plus accumulated interest, meaning that interest outstanding is also subject to interest charges.
The real cost of borrowed money
Because of compounding interest, the total of loan payments is more - sometimes drastically more - than the amount you borrow (note that borrowing often comes with fees as well, but that's not part of interest calculations). Example: if you borrow $1,200 for 12 months, with monthly payments and 6% interest compounding monthly, you'd pay back $103.28 per month over the 12 months for a total payback of $1,239.36. That extra $39.36 is essentially the cost of borrowing money for a year - you had to incentivize someone to let them use their money.
The table below shows a multiplication factor (or interest factor) to arrive at the total cost of borrowed money for a given loan term and interest rate. I'm sure someone else has done this before, but I haven't come across it in my long-tenured financial studies. Share with friends so we can improve financial literacy!
The amounts provided indicate the relationship of total loan payments compared to an original loan amount. You'll see that the higher the interest rate and/or loan term, the higher the multiplication factor. Look at how grotesque the numbers in the bottom right of the table get. Don't want to meet that kind of debt in a dark alley.
Here are a few scenarios to describe how to read the table. All calculations were based on interest compounding monthly.
If you took out 30-year fixed rate mortgage at 7.5% interest and made only the scheduled payments, you'd pay 2.52x the original loan amount (find in the table where 30 year term and 7.5% interest intersect). For a $400,000 loan, the total of payments add up to $1,006,869. Sadly, that doesn't mean the house is worth a million dollars.
If you took out a $100,000 of student loans at 5.00% interest and paid them off over 15 years, you'd pay 1.42x the original loan amount. This means payments would total over $142,000, or 42% more than amount borrowed.
If you financed a bathroom remodel with a 7-year, $50,000 personal loan at 17.5%, it would cost you 74% more than what you paid the contractor (interest factor 1.74x). In other words, that $50,000 project would cost over $87,000 in total.
Wrapping up
Now that you have a visual and some examples for how interest can add up, you can see how borrowing money can get out of hand. Make sure that if you borrow, it's worth it. Borrowing for a responsible home purchase? Yeah, that could make sense. Financing a residential soda machine? Probably not.
In a subsequent post we'll look at how making extra principal payments can be a very effective use of cash. Sneak preview: the longer the term and the higher the interest rate, the more impactful early payoff can be.
Lots of people understand the math of interest, but still have attitudes, behaviors, and choices that keep them paddling against the current. People need perspectives and lifestyles that help them make positive, healthy choices. For a well-rounded and entertaining financial wellness education, please subscribe to the blog and check out my book, Healthy Dough.
Want to run some of your own calcs? Check out calculator.net for easy to use loan calculators, and play around with some specific scenarios. If you don't enjoy building out interest rate factors in MS Excel like I do, this site is an easy place to run individual calcs.
What questions do you have and what other interest-ing math do you want me to demo?
Your best life is a healthy life. Go get it.
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