 Compound Interest – What’s That Mean, Anyway?

What is compound interest and how does it affect you?

Welcome to What’s That Mean, Anyway? — our column explaining financial terms and concepts in a way you can actually understand.

Seems odd, right? A financial company explaining financial terms in a way you can actually understand. Finance is filled with so much jargon it’s like trying to jump into a conversation without knowing the language.

Today’s topic is both good and bad for you — compound interest.

What’s That Mean, Anyway?

Okay, so first to understand compound interest, you need to know what interest is. Also, as a warning, there’s going to be some math.

Ugghh math, but I’m listening.

So interest represents the cost of borrowing money, and it’s usually expressed as a percentage rate. You hear about it most often when talking about loans or watching credit card commercials.

Wait, but I have an interest rate on my savings accounts, and I didn’t borrow that money from my bank.

Well, the bank is actually borrowing that money from you. While your money is in your savings account the bank is using it to fund boring banking things, and as a thank you, they technically pay you.

Oh, that’s great.

Yep. So there are 2 ways people calculate interest — simple and compound. Simple is pretty, well … simple. And because that wasn’t your question, we’re going to skip right to compound interest.

Hooray! Less math.

Just kidding. You walked right into that one. The easiest way to explain compound interest is by comparing it to simple interest. Which requires math, sorry.

Okay fine. What’s the difference?

Simple interest is calculated from the original loan amount. Compound interest is calculated from the original loan amount plus the interest charged.

So compound interest is kind of like “interest on interest.”

Exactly.

Now I’m interested. Bring on the math.

Ha. “Interested.” Nice.

START OF MATH > So say you put \$10,000 in that savings account you have, and your account has an interest rate of 5%. Then immediately after making your deposit you risked your life saving a bus full of puppies and orphans.

That sounds like me.

But although you saved all the orphans and puppies, you hit your head, fell into a coma for 3 years and couldn’t touch that savings account. Let’s see how much money you’d have in your account when you awoke 3 years later as a hero.

Simple Interest

Simple interest is calculated each year only on the original deposit.

Coma Year 1: \$10,000 x 0.05 = \$500 in interest + Coma Year 2: \$10,000 x 0.05 = \$500 in interest + Coma Year 3: \$10,000 x 0.05 = \$500 in interest

Total interest earned while in coma = \$1,500

So as the city throws you a parade when you wake up from your coma, with simple interest, your savings account will have \$11,500 in it.

Simple Interest Equation:

[(original deposit in account) x (interest rate) x (years in coma)] + (original deposit in account) = (new amount in account)
[\$10,000 x 0.05 x 3] + \$10,000 = \$11,500

Compound Interest

Compound interest is calculated each year by adding the interest onto the current total amount in the account.

Coma Year 1 = \$10,000 x 0.05 = \$500 in interest + Coma Year 2 = \$10,500 x 0.05 = \$525 in interest + Coma Year 3 = \$11,025 x 0.05 = \$551.25 in interest

Total interest earned while in coma = \$1,576.25

So as the city throws you a parade when you wake up from your coma, with compound interest, your savings account will have \$11,576.25 in it.

Compound Interest Equation:

[(original deposit in account) x (interest rate)] + (original deposit in account) = (end of year 1 in account)
[(end of year 1 in account) x (interest rate)] + (end of year 1 in account) = (end of year 2 in account)
[(end of year 2 in account)  x (interest rate)] + (end of year 2 in account) = (end of year 3 in account)

[(original deposit in account) x (interest rate)] + [(end of year 1 in account) x (interest rate)] + [(end of year 2 in account)  x (interest rate)] + (original deposit in account) = (end of 3 three in account)

[\$10,000 x 0.05 x 3] + \$10,000 = \$10,500
[\$10,500 x 0.05 x 3] + \$10,500 = \$11,025
[\$11,025 x 0.05 x 3] + \$11,025 = \$11,576.25

[\$10,000 x 0.05] + [\$10,500 x 0.05] + [\$11,025 x 0.05] + \$10,000 = \$11,576.25

< END OF MATH

Wow. That was a lot of math.

Yep, sorry. So with compound interest, you’d earn \$76.25 more while you were recovering from your heroics than you would with simple interest.

I’ll take that.

And the math can get even more complicated if your interest isn’t calculated yearly — it can be calculated monthly, or, like most credit cards, daily. But do you get the baseline of what compound interest is?

I think so. Compound interest is just the interest charged/earned over the life of a loan or deposit that takes into account the interest charged/earned before it.

Like if I took a bite out of an apple. My next bite out of that apple won’t be from the original unbitten apple — which is simple interest — it will be out of the apple I’ve already bitten. Compound interest takes into account what’s already happened and builds on it.

That’s … actually a pretty good analogy. You kind of nailed it.

Got it. Thanks. So that’s what that means.