If you’re looking to effectively manage your finances, one of the most important concepts to master is compound interest. For many of us the math behind it can feel a bit mysterious but this is one particular math problem that can have big implications for your finances. It pays to understand how it works, so sharpen that pencil and embrace the learning the essentials of compound interest.
Compounding Interest in Plain English
When you earn interest on your savings, the bank pays you a percentage based on the amount of principal i.e. the actual amount you have in your account. That interest they pay to you gets added to the money you already have in your account, leaving you with more money than you started with. Nice. Now, if the bank only ever added up interest as a percentage of your original principal, they’d give you the same interest payment every month. This is known as simple interest.
However, most banks operate using compound interest. In this case, every interest payment they make becomes a part of your principal, so the next interest percentage is calculated on the new, larger amount of money you have. This means you make a little more each time, because you’re earning interest on the interest they already paid to you last month.
As you earn interest on your principal, the amount added to the principal (that’s the result of interest paid from the bank to you) gets compounded. So, your wealth grows as a result of interest that’s being compounded month after month.
Compound Interest as a Math Problem
Let’s look at some numbers to see how compounding interest adds up over time.
If have $100 in an account that earns 5% interest annually, how much will you have at the end of the year? Here’s your formula:
P ( 1 + i ) = your principal plus your interest at the end of the year
In this case, $100 ( 1 + .05 ) = $105. (Remember to do the step in parentheses first, then multiply by P).
But this number grows exponentially over several years, because you’re earning interest on your interest. To figure that out, use this formula:
P ( 1 + i ) y = your principal plus interest to the power of “y” over a number of years.
To figure out your total after five years of compounding interest at 5 percent, you solve this: $100 ( 1 + .05 ) 5 = $127.63
Note that this is more than the $25 in interest you’d earn if you calculated simple interest five times instead of using the compounding formula.
Pro Tip for Math Nerds: Your smartphone’s scientific calculator has a button for figuring out the exponent. It looks like X y.
Pro Tip for Math Haters: Try an online calculator to figure out compound interest instead.
What Compounding Interest Means for You
The most important thing to realize about compound interest is that it adds up — big time. This is great when it comes to building your savings: Compound interest helps your money grow faster than it would with simple interest. When you contribute regularly to your bank or brokerage account you can really take advantage of bigger interest payments to work in your favor.
The downside to compounding interest is that it’s also how banks, credit card companies, and other lenders calculate the interest on your debt. You can take the same formulas above to figure out how much compound interest you’ll pay on a credit card bill for a $100 concert ticket. If you let it ride on your credit card for five years at 5% interest, it will end up costing you $127.63.
Of course, most credit cards have interest rates that are much higher than 5%, so proceed with caution! It’s never a good idea to let your debts linger for long. Paying them off quickly allows you to stay ahead of the compound interest curve and create a better financial future.
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