Do you know the difference between compound and simple interest? Learn it here

Math might not be everyone’s cup of tea. However, there are some concepts very important to everyday life. Learning the difference between compound and simple interest, for example, is essential to understand some basic fees related to expenses. 

Have you ever forgotten to pay a bill and, when you went to pay it, it was double the value? That happens due to the interest fees. Learn all about it and its types here, at OneBlinc. Never get surprised about the difference between compound and simple interest again!

First things first: what is interest?

Whenever you create a “pay later” type of debt, such as using electricity for a whole month, paying things with a credit card, or even requesting a loan, you make a deal. Putting it simply, that deal says one thing: “I’ll give you what you need now, but you’ll have until a certain date to pay it back”.

That “certain date” in question will depend on the contract you signed: the electricity bills always arrive at the end of the month, the credit card is due every 15th, and the loan has to be repaid weekly, for example. If that payment is not made on time, the contract will also predict a little fee, which is called interest. 

In some cases, you don’t even have to be late to deal with interest fees. Most loans will automatically charge you interest, but the value only grows if you fail to repay what you owe on time. 

Nevertheless, a curious thing to look out for is that interest fees can be present in two forms: simple and compound interest. Beware, because these two concepts can get your mind twisted and create a bigger problem than they should.

Simple interest

If you’re wondering what simple interest is, as the name suggests, it’s simple. Imagine you owe $100 to a friend. They say that you can repay them on the 2nd week of next month, no later than that. If you fail to repay them on said date, they’ll charge you 10% interest for each week without payment. 

That’s a deal, isn’t it? Then, you remember to ask if they meant simple interest or compound interest because that changes things a bit. Your friend responds: “I’ll go easy on you. Simple interest is good!”.

Back home, a question bugs you: what is simple interest, even? Back to school’s math books, you go. You figure out that, if you don’t pay your friend back in time, they’ll charge you an extra $10 for every week after the set repayment date. How come?

Calculating simple interest

Let’s now translate that little scenario into numbers. After the repayment date, your friend will charge you 10% of the agreed amount ($100) for every week you don’t pay it back. Simple interest is always based on the first amount you borrowed, no less, no more.

That means that, after 5 weeks late, you’ll have to pay your friend $100 + 50%, which equals $150. After 2 months or 10 weeks, you’ll already have to pay $100 + 100%, double the original amount. That math goes on until you finally pay your debt. The mathematical formula to that is:

A = P(1 + rt) 

in which:

• P = the original amount owed;
• r = the interest rate;
• t = the repayment time passed;
• A = the final amount owed.

Compound interest

After you made all the calculations, you drew the conclusion that your friend’s fees were too high. You gave them their money back and figured that a bank would give you better payback conditions. Some time and research later, you find an institution that’ll lend you $100 with the same repayment period.

The only change is that, instead of the 10% simple interest late repayment fee, the bank will charge a weekly 2.5% compound interest fee for every late week. Even with the difference between compound and simple interest, this is way more affordable, right? 

You go back home happily, with your $100 and your new repayment date. Then, 2 months later, it hits you: the loan! It’s already 15 weeks after the agreed repayment date. You rush to the bank, and the amount you now owe astonishes you: $144.83. How can it be?

Calculating compound interest

As you could see, compound interest fees may seem more appealing at first, but the way they act over time is not so pleasant. This type of interest is also called interest on interest because they act upon every new value generated by the last fee. 

That means that, if you didn’t pay your loan on time, on the first week late, you’ll have to pay $100 + interest. Then, the next week, the new interest fee would be added to that value, i.e. ($100 + interest) + interest. That goes on until the debt is paid. The formula is presented like this:

A = P(1+r/n)nt

in which:

• P = the original amount owed;
• r = the interest rate;
• n = number of times the fee has been compounded;
• t = the repayment time passed;
• A = the final amount owed.

Keep learning with OneBlinc!

Now that you know the difference between compound and simple interest, don’t miss out on the chance of learning more about finance! OneBlinc teaches you everything you need to know here, in our blog!