Written by :
May 22, 2020
When I was a kid, about 8 years old, my parents opened up my first savings account. It was around this time that I first heard about the concept of interest. The very idea that I could put $100 into the bank and it would grow by approximately 12% every year, brought tears of joy to my eager eyes.
But then I heard even better news…
If I left that bank account alone for 10 years, and didn’t withdraw any money or make any changes, the money I had earned from the 12% APR would be tacked on top of my initial deposit and together the sum of my earning and my original balance would be used for the interest calculation during the following year. This means that the second year I would make even more money by doing nothing. Just sit back and let my $100 do its thing.
Now if that’s confusing, don’t sweat it. I’m going to unravel it for you in very simple terms.
First things first. I’ll start with the basics.
Topics In This Article
– Topics in This Article –
So You Want to Learn About Simple Interest?
In order to understand compound interest, it helps to have a basic understanding of how simple interest is calculated.
Let’s assume you were to deposit $100,000 into a savings account with an annual percentage rate of 10%.
Now before you start hurling tomatoes at my head yelling obscenities and comments such as “That’s preposterous, get him off the stage!”, let me start by saying this:
I know it’s not the 1980’s anymore and we don’t get savings accounts with this type of return on investment, especially in 2020. However, for educational purposes, it’s just easier to absorb whole numbers in tens, so just roll with me here.
At the end of the first year, you will have earned $10,000. If you were to withdraw your entire profit and leave the original principle of $100,000 in the bank for another year, then at the end of the 2nd year you will have earned the exact same return assuming the 10% interest rate remains static.
Now it’s safe to assume this makes sense to everyone.
All in favour say “Aye Cap’n”!
Simple interest, however, has its limitations. It is a merely a stepping
stone for basic understanding, and can add applicational value, especially when calculating more complex types of interest – such as compound interest – which commonly uses frequency as another variable.
Simple interest, however, has its limitations. It is a merely a stepping stone for basic understanding, and can add applicational value, especially when calculating more complex types of interest – such as compound interest – which commonly uses frequency as another variable.
So You Want to Learn About Compound Interest?
The complexities of compounding interest aren’t very complicated.
Using the scenario above if you were to leave your first year of profits of $10,000 in the account. Then you will have $110,000.
Let’s say you decide to leave your principal and it’s earnings in the bank for a second year, at the same 10% annual return rate then at the end of that year you will have earned a profit of $11,000 and a total balance of $121,000.
Looking at the charts below you can see how this pattern progresses over the next 10 years.
Now you are earning interest on both the principal and previously gained interest. Hence the term interest on interest.
This phenomenon where interest is earned both on the principle and the previous earnings of interest is what we call compound interest.
Even though this is the first example of compound interest, more specifically…
This is an example of “Yearly Compounding”
What happens to our earnings when we change the frequency interest periods? In other words, what happens when we apply our interest rate more often than just yearly?
Is There Such a Thing as a Wealthy Snowman?
I like to think of compound interest in comparison to a snowflake.
Pick up a few snowflakes in your hand, and pack it into a ball. Now roll that ball down a ski slope. Casting aside all things like resistance – in terms of friction, wind or temperature changes, that snowball will keep on a-rollin’ down the hill until it gets to the bottom.
What happens to the snowball as it rolls?
It gets bigger, and bigger, with every snowflake it picks up along the way. Through each revolution, as it continuously rolls down the hill, its size increases.
With the power of compounding, you can compare your potential earnings to a snowflake growing into a snowman. The longer the hill, the bigger the snowman can get from having more time rolling. The steeper the hill, the faster the snowman grows.
Using the above analogy its seems clear that:
- A longer hill = money spending more time compounding.
- A steeper hill = money compounding at a faster rate
However – and this is good news – there’s another way to gain speed.
So You Want to Learn About Compound Interest?
So You Want to Learn About Monthly Compound Interest?
Is It That Time of the Month Already?
Hold the phone!
Another way, you say?
Yup. Using the following formula we can see how compounding interest yearly increases our earnings in comparison to simple interest.
Now, what if we were to increase the frequency from yearly to monthly?
Looking at the chart below, we can see the comparison of all three, from simple interest to compound interest to monthly compound interest.
Simply put, instead of tallying up your interest annually, it’s performed monthly. That is to say, that your interest is added to your account at the end of every month. So using the same numbers from the previous example, our first month’s earnings would be $833.33, which is 1/12th of the total year’s interest.
After stacking the interest on top of your initial balance, you can see that your new balance at the end of the month corresponds to $100,833.33. Moving forward through each month – from February to March and so on – it’s easy to discern how successive growth is of an exponential nature.
This makes for some sweet returns using functional mathematics.
As you can see the difference that your financial institution pays you, over the course of one fiscal year, for maintaining an account that compounds monthly vs. yearly is $471.31.
That’s roughly 10 nights at the movies using your Scotiabank Scene Visa complete with 2 cold bevvies of your choice on the rocks and a large buttered popcorn. Not that buttery flavoured garbage – the real stuff!
So at this point, you’re asking yourself can we get a little deeper with this?
Why yes, of course, you can. Which brings us to our next and final frequency rate of compounding.
So You Want to Learn About Compound Interest?
So You Want to Learn About Daily Compound Interest?
The Daily Show
(Without Jon Stewart)
With daily compounding, you’re just taking monthly values and stepping it up a notch. All of the rules still apply except in this case the interest is added at the day’s end.
As I’m sure you’ve already noticed, the differences between accounts that are compounded annually vs. monthly are negligible. Likewise, the difference between monthly and daily compounding follow suit. You’d have to deposit a rather substantial amount of money in today’s markets to have any sort of profit worth writing home to mom about.
Notice the values in the chart comparing all four methods of calculating interest.
This assumes all things remain equal, which isn’t necessarily realistic since life always gets in the way. When we make a withdrawal or a deposit we are effectively changing the interest rate daily or as often as you make a transaction.
It’s nice to know that all these calculations are not made by an individual but by hardware and software. A server for the lender which processes these transactions as they occur “on the fly” constantly adjusting the output through the continuous fluctuations of +‘s and -‘s
Yes, today’s interest rates for savings accounts are somewhat of a joke. Be that as it may, the flipside of the coin is that you might have an opportunity to benefit from these low rates when borrowing. I say might, concerning the multitude of rates that are available to choose from when determining which credit card or mortgage is right for you. Not always, however, so it’s crucial that you do your homework.
Figure out why you’re borrowing and how long you’re going to be borrowing for so that you are well informed enough to choose an interest rate that would suit your needs. Have a goal and write it down.
What is The Impact of Compounding on Credit Cards?
When considering interest rates, be it simple, compound or complex, you’re either on the giving or the receiving end of the investment income.
For the length of this article, we’ve considered you – the reader – as you the receiver, or you the lender. That is to say, you have made your capital income available to the bank in return for a daily, monthly or yearly guarantee of earnings through interest.
But what happens if we switch teams?
When you become the borrower?
In situations like this, you’re either applying for a student loan, auto loan, mortgage or a line of credit.
In this case, of course, the lender is the bank or whichever financial institution you have associations with. So it’s crucial that you educate yourself with the terms of service.
What I mean by that, is your top priority is to learn the specific rules set up by your bank. These rules can determine how much money you spend or save on interest, especially in scenarios where there is a high Annual Percentage Rate.
Consider these 5 FAQ’s put forth by our dedicated readers:
- How frequently is interest compounded with this type of account?
- What is the A.P.R.?
- Are there any grace periods allotted?
- What penalties are there for missing payments?
- What is the real danger when getting careless with borrowing money?
How is Credit Card Interest Calculated?
How Frequently is Interest Compounded?
Credit cards which are a type of revolving credit commonly have a monthly billing cycle, however, the interest that is charged to your account accumulates daily. As such, lenders of financial institutions utilize the “daily compounding “ form for their calculations.
What is The A.P.R.?
A.P.R. is an acronym which stands for Annual Percentage Rate. When you apply for a new credit card you’re quoted a rate which is based on a yearly calculation. However, since the interest on credit card balances accrues on a daily basis you have to divide the interest rate by 365 days (some credit card issuers use 360 days), to get the daily rate.
As an example, let us say you have a Scotiabank Visa with an interest rate of 19.99% A.P.R. and you want to find out what the daily rate is. You would have the following formula:
Now multiply this rate by your current balance to find out how much interest was added on that day. Once you find your daily interest charges you then add that to your balance to produce your updated daily balance.
As an example, let’s pretend we have a balance of $7,800 on our visa. This is our formula:
If you want to do it again just follow the same formula with the new daily balance – which now includes the previous day’s interest charges.
In reality, the calculations are a bit more complex than this. We haven’t taken into account any new charges and purchases nor have we considered any credits or payments to the account.
You would need to perform these calculations every single day, adding the interest charges and then adjusting for any additions from new purchases, cash advances, balance transfers, and any Scotiabank credit card cheques then subtract for any credits or payments applied to the account.
This is how a financial institution’s internal system functions.
Fortunately, all of these calculations are performed by the bank’s computers using sophisticated software to avoid mistakes and stored on their servers.
When we view our balances and daily transactions that appear in our mobile and desktop online banking apps, the daily interest that is generated by the system is not displayed to us until the end of the billing cycle.
So the bank’s servers have to store a hidden balance that is not visible to the customer. Throughout the month, as more and more debit or credit transactions occur, the bank’s software unobservably tallies this balance using the daily rate formula as stated above and follows this “shadowed” balance which then becomes visible to the cardholder when the final monthly bill is produced.
Are There any Grace Periods Allotted?
Typically most credit card issuers allow an interest-free grace period of anywhere between 21 and 25 days. The most frequently offered time period is ordinarily 21 days but I’ve seen a few financial institutions provide slightly more time.
Keep in mind, with respect to grace periods, there are two important elements of to consider:
- If you have an outstanding balance prior to making new purchases with the account and don’t plan on paying it off in its entirety before the grace period is over, then any new payments made after those purchases might not offer you the possible savings you were intending for.
Interest-free grace periods are only available with regular purchases. Unfortunately, this doesn’t apply to cash advances, balance transfers, and credit card checks. For these types of transactions, interest is compounded daily, starting from the 1st day and moving forward until the balance is paid in full.
Interest-free grace periods are only available with regular purchases.
Unfortunately, this doesn’t apply to cash advances, balance transfers, and credit card checks. For these types of transactions, interest is compounded daily, starting from the 1st day and moving forward until the balance is paid in full.
- If your credit card issuer has a grace period of 21 days, and you decide to make a payment on the 20th day after your purchase, then you would indeed be walking the tightrope.
You’re better off making a payment with 4 or 5 days to spare. Perhaps on the 15th or 16th day after you’ve made your purchase. In this way, you would reap the benefits of savings by avoiding interest that accumulates after the grace period ends.
Online banking definitely has its advantages. Quite often payments can take 2-3 days to be applied towards an account. I’ve even seen payments applied within 24 hours after submitting through an app or desktop.
Internal payments are much quicker. For instance, if you were to apply funds to an RBC Visa from an RBC Savings Account using your smartphone. It would be judicious to take this into consideration.
Try testing it out for a couple of months to see how quickly payments are processed by the credit card issuer at hand.
What penalties are there for missing payments?
If you miss your payment or fail to produce a minimum payment by the due date you’ll most likely incur a late fee anywhere between $20 and $40 depending on the issuer.
You can expect an increased A.P.R. if your account becomes 60 days past due. You don’t want to find yourself in this scenario, otherwise, all of your hard work trying to understand interest rates and how they are applied will amount to nothing.
To top it off, it will be reported to the credit bureau and will most likely affect your score negatively.
Credit card interest is a big deal. Do not take it lightly. With the effects of compound interest, it’s easy to see how your monthly charges can quickly get out of control.
Without a clear plan you risk:
- Ruining your credit score
- Accumulating excessive amounts of debt
- Being able to afford large payments that only get applied to interest charges and still have a continually high monthly balance
- Being tempted to purchase items with money that isn’t yours
Having a balance of $5000 with a 21.99% interest rate is easily equal to one week’s worth of groceries for some people. For many individuals, this just isn’t an option.
Unless you are willing and able to pay off your entire balance each and every month you should consider a card that is specifically geared to those individuals who require more flexibility.2
Choosing a low-interest credit card that’s right for you isn’t such a hard task and if it’s something that you feel would be beneficial to your situation, then isn’t it worth considering?