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# Compound Interest vs. Simple Interest

What we’ll cover:

• Simple interest is calculated by multiplying your balance by the interest rate
• Compound interest is a little more complex because interest gets added to the balance and the interest rate gets applied to that heftier balance, letting you earn more interest

The difference between compound interest vs. simple interest could be significant and will determine how fast your money grows in a savings account, or how quickly interest accumulates on a loan. While compound interest is generally discussed when talking about savings, it could be a good concept to keep in mind when you borrow money as well because the way rates are applied influence how much interest could get tacked on.

## What is simple interest?

Simple interest is pretty straightforward in that you multiply your balance by the simple interest rate.

For instance, let’s say you wanted to borrow \$10,000 from your friend. Your friend agrees, under the condition that you pay them 5% in interest for the year. You get the money from your friend, and in exchange for lending you money, your friend pockets \$500 in interest.

Now, let’s say the next year comes around and haven’t paid back any of the loan yet. You ask to extend the loan and keep the same annual interest rate. Now your friend will earn an additional \$500 for that second year, for a total of \$1,000.

Here’s how we got to \$500 per year owed in simple interest.

### Simple interest formula:  A = P(1 + rt)

• P = principal balance
• r = interest rate (converted to a decimal, for example above of 5%, 5/100=.05)
• t = time (in years)

For our example above with your friend’s loan of \$10,000:

• One year: \$10,000 (1 + .05 x 1) = \$500 in interest
• Two years: \$10,000 (1 + .05 x 2) = \$1,000 in interest

This may sound like a decent chunk of change to give a friend, but you’re getting kind of a deal with this arrangement. If you compare simple interest vs. compound interest, you’ll actually pay less in total interest when you’re just paying simple interest.

## What is compound interest?

So simple interest is kind of like a no-frills approach to interest – this is the balance, this is the interest rate, end of story.

Compound interest is more dynamic because interest gets added to the balance. When you’re saving, compound interest has a nice stickiness to it – interest gets added to the balance and the interest rate gets applied to that heftier balance, letting you earn a larger amount of interest.

So, say instead of borrowing \$10,000 you instead save \$10,000, and, for the sake of symmetry, say you find a savings account that pays 5% (if you do, call us). We’re also going to assume you don’t touch the money in that account while interest accumulates.

To shake things up and show how compound interest works, we’re going to say that instead of earning that 5% once a year, interest will compound daily. So each day, interest is accruing on both your principal balance, plus the interest you earned the previous day. This means that every day your balance gets a little bit bigger, and the interest rate is applied to this growing balance every day, earning a larger amount of interest.

In 12 months you’ll have earned \$513 in interest. In 24 months, you’ll earn an additional \$539 in interest, pocketing a total of \$1,052 just for letting your money sit. Consider how much this money can grow if you leave your money in the account for a number of years.

With simple interest, which means the interest you earn isn’t added to the balance, you’d have earned less interest for the same amount of effort.

Now, here’s what’s the calculation for compound interest.

### Compound interest formula: A= P (1+ r/n) ^ nt

• A = total balance, principal amount plus the interest earned
• P = principal balance
• r = interest rate (converted to a decimal, for example above of 5%, 5/100=.05)
• n= number of times interest is applied per time period
• t= time, number of time periods in which your money is invested or borrowed

For our example above, here are the numbers we used:

• One year: (or day 365): 10,000 x (1+0.05/365)^(365*1) = \$10,512.67 in interest
• Two years: 10,000 x (1+0.05/365)^(365*2) =  \$11,051.63 in interest

## Compound interest vs. simple interest – which one do I want when looking for an account?

So the next time you’re shopping around for a savings account or a loan, take a look at a few things: whether it’s simple or compound interest, and if it’s the latter, how often it compounds. And then finally, look at the actual number of interest rate. These factors can make a big difference.

And friendly reminder (okay it’s a shameless plug) . . . interest compounds daily for Marcus’ high-yield Online Savings Account and CDs. You can use our savings interest calculator to see how much money you could earn in interest with an Online Savings Account. ### Saving for your future starts today. See how Marcus can help.

This article is for informational purposes only and is not a substitute for individualized professional advice. Articles on this site were commissioned and approved by Marcus by Goldman Sachs®, but may not reflect the institutional opinions of The Goldman Sachs Group, Inc., Goldman Sachs Bank USA or any of their affiliates, subsidiaries or divisions.

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