Most of us have a love/hate relationship with interest. If we’re borrowers, we hate interest. If we are savers, we love interest.
The ancient Greek philosopher Aristotle thought interest was terrible. The brilliant physicists, Albert Einstein, thought interest was the 8th Wonder of the World!
Emotions aside, smart business owners should understand the difference between simple and compound interest. Like Benjamin Franklin said, an investment in knowledge pays the best dividends.
What Is Interest?
While interest is something that all of us accept as a normal part of our financial lives, it’s been a controversial practice for centuries. Many religious texts – including the Bible, the Torah, and the Koran – forcefully caution against it.
Interest is the cost of using someone else’s money. When you deposit money in the bank, the bank pays you for the privilege of using your money. You’re lending money to the bank. It feels good to think about it that way.
Did you know that your deposits are considered a liability by banks? This is because banks don’t own your money, they’re borrowing it from you. When you take out a loan, you don’t own that money, you are borrowing it from the bank. Both you and the bank charge interest for the privilege of using the other’s money.
When you take out a loan from a bank, you pay the bank for the privilege of using their money. Banks make money by charging you more for loans than they pay you for deposits.
Important Terms to Know
Have you ever read the fine print on your mortgage or car loan? Of course, you have! The terms used throughout this post are basic, but here are a few important refreshers:
- Principal is the amount of money borrowed or deposited
- APR is the annual percentage rate
- Term is the amount of time money is borrowed or deposited
- Amortization is a repayment schedule on an installment loan
There are two ways to calculate interest:
- Simple-interest method
- Compound-interest method
How does compound interest differ from simple interest? Let’s find out.
The simple-interest method of calculating interest is most often used for loans. That’s good news because it is generally less expensive than the alternative.
It’s calculated by multiplying the daily interest rate by the principal by the number of days that elapses between payments.
Interest = Principal x Interest Rate per Year x Time in Years or Fraction of Years
Let’s say you’ve borrowed or deposited $10,000 with an APR of 3 percent. The daily interest would be 10,000 x (0.03/365) = 0.82 or 82 cents per day. Over a 30-day month, interest would be $24.60.
You earn interest on the principal only. It’s rare for saving and investment accounts to pay simple interest, but let’s take a quick look at what this would look like.
Let’s say you have $8,000 in cash that you don’t need for a year. Your bank offers a savings account with a 2 percent APR. If you leave the total principal amount of $8,000 in this account for the entire year, you would earn $8,000 x 0.02 = $160.00 in interest. At the end of the year, you withdraw $8,160.00.
You pay interest on the principal only. Installment loans with set repayment schedules – like small business term loan or vehicle loan – often use the simple-interest method.
These types of loans are often repaid in monthly installments. Borrowers receive an amortization schedule that shows how much principal and interest you pay each month. The total amount you pay each month will be the same, but the breakdown of principal and interest will vary each month.
Let’s say you take out a $100,000 term loan for your small business. You agree to a 1 percent annual interest rate for 3 years. You pay $1,000 in interest for each of the three years for a total of $3,000 in interest. The amount you pay to the bank is $100,000 in principal plus $3,000 in interest for a total of $103,000.
In the example above, you and the lender know exactly how much interest you’ll pay during the life of the loan. The amortization schedule spreads the fixed amount of principal and the fixed amount of interest over a fixed amount of time.
Note that interest in the second year is not affected by interest in the first year. This is a key feature of the simple-interest method and what distinguishes it from compound interest. Read on to see how.
The most basic definition of compound interest is interest on interest. Banks use this method to apply interest to savings accounts. They also use it to charge interest on credit card accounts. Interest accumulates month to month to become part of the principal balance.
For a savings account, each month you don’t withdraw, the principal amount grows, which is great! For a credit card account, each month you don’t pay off, the principal amount grows, which is expensive!
Let’s take a look at some examples. It’s more complicated to manually calculate compound interest but you’ll find plenty of compound interest calculators online. Link
You earn interest on interest. As interest accrues based the amount of the principal balance, this interest is added to the principal balance each successive period.
Building on our example from above, let’s say you have $8,000 in cash that you don’t need for 4 years. Your bank offers a certificate of deposit account with a 2 percent APR compounding annually:
8,000 x 0.02 = 160
8,000 + 160 = 8,160 is the new principal balance at the end of the first year
8,160 x 0.02 = 163.20
8,160 + 163.20 = 8,323.20 is the new principal balance at the end of the second year
8,323.20 x 0.02 = 166.46
8,323.20 + 166.46 = 8,489.66 is the new principal balance at the end of the third year
8,489.66 x 0.02 = 169.79
8,489.66 + 169.79 = 8,659.45 is the new principal balance at the end of the fourth year.
The bank could also compound interest more frequently, say monthly. The more often the bank compounds, the more you will earn. If you put $8,000 in a 2 percent APR certificate of deposit that compounds monthly, how much more would you earn? Let’s take a look.
8,000 x 0.02 = 160
160/12 = 13.33
8,000 + 13.33 = 8,013.33 is the new principal balance at the end of the first month
8,013.33 x 0.02 = 160.27
160.27/12 = 13.36
8,013.33 + 13.36 = 8,026.69 is the new principal balance at the end of the second month
8,026.69 x 0.02 = 160.53
160.53/12 = 13.38
8,026.69 + 13.38 = 8,040.07 is the new principal balance at the end of the third month
And so on….
When compounding monthly, the new principal balance at the end of the twelfth month is $8,161.47. When compounding annually, you only earned $8,160 for the same principal and amount of time invested.
You pay interest on interest. Compounding interest on borrowed money is more expensive than a simple-interest loan. Remember our $100,000 term loan with an APR of 1 percent for 3 years?
Let’s see what this loan costs you if the lender compounds interest annually over 3 years.
100,000 x 0.01 = 1,000
100,000 + 1,000 = 101,00 is the new principal balance at the end of the first year
101,000 x 0.01 = 1,010
101,000 + 1, 010 = 102,010 is the new principal balance at the end of the second year
102,010 x 0.01 = 1,020.10
102,010 + 1,020.10 is the new principal balance at the end of the third year
Compared to the simple interest example where you paid 3,000 for 3 years, the compound interest loan costs you 1,000 + 1,010 + 1,020.10 = 3,030.10 in interest over three 3 years if compounded annually.
Now that you’ve seen the power of compounding, let’s look at where compounding interest can really hurt you: carrying a balance on your credit cards. Imagine you are reviewing your credit card bill.
This month’s balance is $9,000 but you only pay $1,000. Your APR is 18 percent but since credit cards compound interest daily, your daily periodic rate is 0.00049 percent.
You begin your next statement period with an 8,000 balance. You don’t purchase anything on the first day of the new statement period, but your balance still goes up because of daily compounding: 8,000 x 0.00049318 = 3.95.
You start the second day of your statement period with a balance of 8,003.95. The next day you spend $90 for new headphones:
8003.95 + 90 = 8093.95
8093.95 x 0.00049318 = 3.99
8093.95 + 3.99 = 8097.94
The following day you spend $50 on dinner:
8097.94 + 50 = 8147.94
8147.94 x 0.00049318 = 4.018
8147.94 + 4.018 = 8,151.95
Even if you didn’t make any purchases on your card this month, and you started with an $8,000 balance, your balance would increase every day.
Love or Hate?
Without a doubt, you see why we have a love/hate relationship with simple and compound interest. Mostly love….if you’re a saver! Mostly hate….if you’re a borrower.
Understanding the difference between simple and compound interest helps you maximize the good kind of interest and minimize the bad kind of interest.
If you only remember one thing from this post, let it be Benjamin Franklin’s wisdom that those who understand compound interest earn it and those who don’t understand it pay it!