What Is Compound Interest? Definition And Examples
We all like the thought of earning interest on our savings and investments. Equally, we all hate having to pay interest on loans and debts. With some deft mathematical footwork it's possible to cancel out the interest on your debts by using the compound interest that accumulates on your savings.
Let me ask you a question. Do you really understand what compound interest means and how it works? Most importantly: do you know how it can benefit you?
No? In that case let's look at the basics of compound interest. Then we'll look a little at the formula for compound interest. Once we've got through that, you'll be ready to have a play around with some figures using our compound interest calculator. Anyway, let's start with how it works:
What is compound interest?
Here's an explanation that should make everything crystal clear:
When you take out a loan, interest is calculated for the first period (be it a month or a year). This interest is then added to the original total. Following on from that, the interest for the next period is calculated but is based on the gross figure from the first period. From there, well, you get the idea.
It does sound complicated. So, as it's often said a picture paints a thousand words, here's an illustration:
Compound interest example 1
Let's say you borrow $2,000 over a 3 year period, pay 10% annual interest on your debt and are not making regular repayments. In this case, the amount you will have to repay will look like this:
Year 1: $2,000 x 10% = $200.
Year 2: $2,200 x 10% = $220.
Year 3: $2,420 x 10% = $242.
The total repayment figure after 3 years is $2,662 (the $662 interest is the sum of each year's interest).
It should be noted that if you make regular repayments on your loan, the total compound interest will be lower because the remaining principal on the loan will be decreasing at each compound interval. We have a loan calculator if you want to try out some figures.
Compound interest example 2
Let's look at it with a simple $500 yearly repayment figure added in:
Year 1: $2,000 x 10% = $200. Total is now $2,200.
Year 2: ($2,200 - $500) x 10% = $170. Total is now $1,870.
Year 3: ($1,870 - $500) x 10% = $137. Total is now $1,507.
The total repayment figure after 3 years stands at $1,507 and the interest paid by the end of year 3 is $507.
The benefit of compound interest
This seems like a good time to feature a diagram to help demonstrate the power of compound interest in a positive way. The graph below shows the result of $1000 invested over 20 years at an interest rate of 10%. The principal figure is in green. The blue part of the graph shows the result of 10% interest without compounding. Finally, the purple part demonstrates the benefit of compound interest over those 20 years.
One point to consider when you do the math is something called "compounding frequency". In a nutshell, this is the frequency at which your interest is calculated annually, e.g. every month, every quarter, every twelve months, etc. Knowing the periods at which the interest is calculated will ensure your calculations are accurate.
If you want another way to work out the figures (one that's sure to impress some of your friends with your mathematical skills) then take a look at the formula:
The formula for compound interest
The formula used to calculate standard compound interest (including the principal) is as follows:
M = P( 1 + i )n
M is the final amount you repay at the end of the loan.
P is the principal amount you borrow.
i is the annual rate of interest.
n is the number of years you borrow/invest over.
If we use the example of our $2,000 borrowed at 10% over 3 years (without repayments) we get the following calculation:
M=2000(1+0.1)3 = $2,662
Working out what you're going to pay on any loan or debt is an exceptionally useful way of gauging the best money deals available to you. But let's take this a little further.
You see, compounding interest on what you owe is only one way of looking at how this interest mechanism works. But what if you have have very little, or no, personal debt. If you're in this financial position then you're probably asking yourself this question...
How can compound interest help you?
Having the ability to work out the best offers is a great advantage. But what if you're looking to make some investments? You've worked hard for years and your savings fund is looking incredibly healthy. Sadly, you know that, at the current interest rate, the cash you're putting away for your retirement might not cut it.
Once again, the power of compound interest can be used on your money. This time it's going to help you, rather than topping up a lender's coffers.
Here's how (and you'll be surprised how simple it is).
Compound interest holds great benefits for long term savers.
To put it in simple terms, the interest you earn on any savings and investments is accrued in exactly the same way as it is on money you borrow.
So, using our example of $2,000 invested over 3 years at 10% will give you an accumulated figure of $2,662. Basically, you're getting paid to do nothing more than keep your money in one place. You don't need to juggle finances. You don't need to try and calculate monthly or annual returns - it's all done for you.
At its simplest, the investment vehicle you put your money into will give you interest on the interest they've already paid you. Money for nothing - seems like a good deal. And the banks just keep on giving. As long as you leave your money in an account, it will continue to accrue interest. What's more interesting is how quickly you can double your money (something you'll no doubt be very interested in learning). The banks have a simple formula you can use. It's the "Rule of 72" and it works like this:
The rule of 72
Kalid Azad from the website Better Explained has a great article about the rule of 72 that's well worth reading. The concept is that you divide the 72 by the interest your savings are earning. For example, let's say it's 3%. Divide 72 by 3 which will give you 24. So, in 24 years your initial investment will have doubled. If you're receiving 6% then your money will have doubled in 12 years.
This might seem like a long time but, considering most of you should be planning for your retirement in 20, 30 or 40 years time, it's a comparative drop in the ocean.
Admittedly, interest rates will rise and fall. Any investments and savings you're going to rely on in later life should be scrutinised very carefully. At a minimum, you should be carrying out an annual review of the health of your cash flow. If you can find a better deal elsewhere then seriously think about moving your money - after all: it's your cash and your future.
To make things a little more simple, you might want to take a look at our aforementioned compound interest calculator tool. If nothing else, it'll save you time and effort.
Written by James Redden
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Last update: 02 November 2018