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Simple & Compound Interest

Interest is a percentage of a loan or debt (credit card balance, student loan, etc.) that is charged to the borrower for the service and convenience of borrowing money. Interest is also earned on investment products (savings accounts, share certificates, money market funds, etc.) by investors. But, the type of interest and how often it’s accrued, or charged, can mean the difference between a lucrative investment or a poor one, and between a good deal on a car loan or a bad one.

Here’s what you need to know about the two types of interest—simple and compound—so you can minimize the rates you pay on loans and maximize the money you make on investments—even if it’s just which type of savings account to open.

Simple Interest

Simple interest is good news for borrowers but less than ideal for investors because it’s calculated based on the original principal only of the loan or investment. Car loans, certificates of deposit (CDs), and some department store financing on large appliances are examples of loans and investments that use simple interest.

Say you deposit $10,000 into a savings account that earns 8 percent simple interest for 3 years. Here’s how much interest you would earn over those 3 years:

Interest earned in year 1: .08 x $10,000 = $800

Interest earned in year 2: .08 x $10,000 = $800

Interest earned in year 3: .08 x $10,000 = $800

Total interest earned: $800 x 3 years = $2,400

It’s not a terrible profit, but you could make more if your investment earned compound interest.

Compound Interest

Compound interest is earned on the original investment or loan principal plus all the interest earned so far. It’s often explained as earning or charging “interest on interest.” Applying interest on top of interest grows the sum at a much faster rate that picks up speed and size with time—like a growing snowball. This is what’s often referred to as the “miracle” or “magic” of compound interest. It’s how things like retirement investments work and why it’s important to start saving as soon as possible—or pay off a loan with compound interest as soon as possible to avoid being crushed by the growing debt snowball.

Let’s see how much $10,000 in a savings account earning 8 percent compound interest, compounded annually, would earn in 3 years:

Interest earned in year: 1 = .08 x $10,000 = $800

Interest earned in year: 2 = .08 x $10,800 = $864

Interest earned in year: 3 = .08 x $11,664 = $933.12

Total interest earned: $2,597.12

That’s a difference of $497.12 from the savings account that only earned simple interest. The longer this savings account earns compounding interest, the bigger and faster the total will grow.

The last part of compound interest to understand is the frequency, or how often, the compounding happens. In the example above, the interest rate was compounded annually, or once a year. The more compounding periods in a year, the more interest earned (or paid if it’s a loan). Common compounding periods include yearly, semi-annually (every six months), quarterly (every three months), monthly, and daily.

As an example, here is the growth of $10,000 at 8 percent interest compounded at different frequencies:

Time

Annual Compounding

Quarterly Compounding

Monthly Compounding

1 year

$10,800

$10,824

$10,830

5 years

$14,693

$14,859

$14,898

10 years

$21,589

$22,080

$22,196

As you can see, the investment or savings account with interest compounded monthly will make much more money for its owner!

Common compounding schedules for various investments, savings accounts, and loans:

  • Savings account: daily
  • CD or share certificate: daily, monthly, or semi-annually
  • Money market account: daily
  • Mortgages, home equity loans: monthly
  • Personal, business loans: monthly
  • Credit cards: monthly

An important note: Interest on an account may be compounded daily but only credited, or added, to the account monthly. It’s only when the interest is actually added to the account that it begins to earn additional interest.

Knowing all of this information means you’ll understand tricks to save money on a loan with compound interest, like this one: If you make half your mortgage payment twice a month—instead of the total amount once a month—you can end up paying off your mortgage early and saving serious cash on interest!

APR vs. APY

Annual percentage rate (APR) is the annual rate of interest on a loan or investment not including the compounding of interest in that year. So even if a credit card lists the interest rate at 11 percent APR, that interest rate could be compounded semi-annually, quarterly, or monthly—which, as we learned above, makes a big difference in how much you end up paying in interest!

Annual percentage yield (APY), on the other hand, does include how often an interest rate is compounded within a year. Another term for APY is earned annual interest (EAR). When considering a credit card or loan offer, be sure to look at APY to get a more complete picture of how much interest you’ll be charged.

Let’s look at some examples to further understand the difference between APR and APY.

What You Actually Pay in Interest (APY)

Credit Card Rates

Quoted APR

Compounded Semi-Annually

Quarterly

Monthly

5%

5.06%

5.09%

5.11%

7%

7.12%

7.19%

7.23%

9%

9.20%

9.30%

9.38%

It’s in the credit card company’s best interest to quote you the APR as it will be the lower number and will encourage you to sign up for the card. For you, it’s in your best interest to always look at the APY as a borrower and as a saver or investor.

Now that you know about simple and compound interest, and APR vs. APY you’ll be a savvier investor and borrower!

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