This week’s topic is another question from a National Financial Capability Study performed in 2024 (two of my past articles highlighted principles from two other questions in this survey - check them out here and here).
As a refresher - in this study approximately 500 individuals from each state and the District of Columbia were surveyed and, as part of the survey, the participants were posed several financial-knowledge questions.
One of the questions touched on the topic of compound debt and only 29% of those surveyed answered correctly.
Here’s the question - do you know the answer?
Suppose you owe $1,000 on a loan and the interest rate you are charged is 20% per year compounded annually. If you don’t pay anything off, at this interest rate, how many years would it take for the amount you owe to double? A) Less than 2 years B) 2 to 4 years C) 5 to 9 Years D) 10 or more years E) Don’t Know
At first glance, someone may think “20% is 1/5, so at 20% per year it’ll take 5 years for the amount owed to double”.
This, however, is not correct.
If you’ve read my articles for a while you may recall one of the first articles I wrote related to compounding gains (you can find that here) where the gains of interest over many years can turn relatively insignificant amounts today into income streams later in life.
Unfortunately for debtors, this compounding principle works both ways: compounding gains for creditors and compounding amounts owed for debtors.
So, in the situation posed in the question, instead of taking 5 years to double it would take less than five years:
Year 0: $1,000
Year 1: $1,200
Year 2: $1,440
Year 3: $1,728
Year 4: $2,074
In less than four years, the amount owed has doubled.
This is because the interest of previous years accrues interest in subsequent years.
This compounding effect is generally present on many loans that an average person may consider - credit cards, financing new furniture/appliances, car/boat/ATV loans, etc.
Most creditors probably wouldn’t allow debtors to not make any payment at all; however, the concept applies to making payments on any less-than-full amount.
For example, in our $1,000 at 20% per year scenario, if the person only paid $100/year the balance owed would look something like this:
Year 0: $1,000
Year 1: $1,000 - $100 = $900; Interest on $900 = $180; Total owed = $1,080
Year 2: $1,080 - $100 = $980; Interest on $980 = $196; Total owed = $1,176
Year 3: $1,176 - $100 = $1,076; Interest on $1,076 = $215; Total owed = $1,291
Even though the debtor is paying $100/year, the overall balance owed continues to increase.
The debtor would need to pay even more to just “break even” each year, and even more than that to ensure that the debt is eventually paid off.
(This is the principle that the “minimum payment” on credit cards follow - if you pay the “minimum payment” each month, you’re not simply splitting up the cost of your purchase over a number of months, you’re paying interest on interest on interest on interest at an amount just above the “break even” amount so that eventually your balance will come down to $0, but all the payments it takes to get there often mean you end up paying multiple times the original balance on the card.)
So, while it’s great that you can invest money and see compound gains - turning $5 of spending money each day now into $83 of spending money each day after 30 years - remember that the principle works in reverse.
If not paid in full, debts with compounding interest will grow faster than “interest rate multiplied by original loan amount” due to the unpaid interest you owe “this year” factoring into the interest you owe for “next year” and so on.
To end back where we started - the $1,000 loan accruing interest at 20% annually will double in: B) 2 to 4 years.
Just remember: interest today will create more interest tomorrow (which will create more interest the next day and so on and so forth).
Make sure that the interest in your life is working for you - providing you with gains on investments - and not working against you in the form of debt that can quickly spiral out of control if not sufficiently paid down.