What is compound interest and how is it calculated? A guide

Interest plays a significant role in borrowing, saving, and investing, so understanding how it's calculated is important. Compound interest is one way interest can be calculated, compared with simple interest. Compound interest adds the accrued interest to the principal, so the next time interest is calculated, it is based on the combined amount.

How does compound interest work?

When compound interest is applied to a sum of money, the accrued interest is added to the balance. It's often used in savings accounts, where the interest earned is deposited into the account. The next time interest is paid, it uses the combined amount as the new balance.

This amplifies the effect of the interest, and the amount it's applied to can grow very quickly. The more frequently compounding occurs, the faster money can grow.

For instance, if you deposit $1,000 in a compounding savings account with 10% annual interest, you'll earn $100 in interest at the end of the first year.

• $1,000 x 0.10 = $100 in earned interest.
• Original balance ($1,000) + earned interest ($100) = $1,100.

In the second year, you'll earn 10% interest on $1,100, your new balance.

• $1,100 x 0.10 = $110 in earned interest
• $1,100 + $110 = $1,210 total new balance.

Without adding additional money to the account, you would earn more interest each year.

Compound interest formula

To help you figure out how much you can earn – or will owe – in interest, you can plug in numbers to the compound interest formula. Let's look at the formula for compound interest:

B = P x (1 + R/N)^(N x T)

Where:

• B: Ending balance
• P: Initial principal
• R: Annual interest rate
• N: Number of times each year that the interest on an investment or loan compounds
• T: Length of time you’ll have the investment or loan

Using our previous example, if you deposited $1,000 into a savings account with compounding interest at 10% for 5 years, your final balance would work out like this:

B = $1,000 (1+ 0.1/1)^(1 x 5)

B = $1,000 (1.61051)

B = $1,610.51

You would earn more than $600 over 5 years.

Compound interest vs. simple interest

Credit cards commonly use compound interest. Let's say you have a credit card with a 22% annual interest rate that compounds daily. At a 22% annual rate, you are charged 0.006027% a day.

If you owed $10,000, your balance after one day would be $10,000.60. You'd then pay interest on that amount the next day. By the end of 30 days, the balance will have grown to $10,183.33.

This is one reason it can be difficult to pay off credit card debt, as the interest you owe compounds.

Unlike compound interest, simple interest is calculated based solely on the loan balance. When you're paying a loan, the interest rate is applied to the balance to determine how much interest you pay.  

Mortgages apply simple interest when calculating your monthly payment. Say you borrowed $350,000 at 6% annual mortgage interest on a 30-year mortgage. Your annual interest rate is divided by 12, then multiplied by your balance to get your monthly interest payment.

$350,000 (0.06 / 12) = $1,750

Lenders determine your monthly payment using amortization, which calculates a total payment amount that allows you to pay off the entire loan amount in the loan term, which is 30 years in this case. The monthly amortized payment is $2,098. So once you pay the interest, $348 is left to apply to the balance.

So the next month, your mortgage balance is $349,652. The rate is applied again:

$349,652 (0.06 / 12) = $1,748

This leaves $350 to apply to the balance. The amount of interest you pay would decrease slightly with each payment, while the amount that's applied to your balance increases. This continues until you pay off the entire balance with the final payment of your 30-year mortgage.

How can you tell if interest is being compounded?

If you want to confirm that an investment account or credit card has compound interest, look at a recent statement.

Before agreeing to a loan, look at your amortization schedule. This shows exactly how interest and principal are paid off. It also shows how much you'll pay in principal and in interest, and the total interest over the life of your loan.

An account with an annual percentage yield (APY) uses compounding interest in its calculations. In contrast, the annual percentage rate (APR) is a disclosure representing the cost per year of a loan, including simple interest and fees.

What are the pros and cons of compounding interest?

Let's look at the advantages and disadvantages of compounding interest:

Pros

Here are some benefits of a savings account or investment with compound interest.

• Build your savings faster: As it goes with savings and earning money in interest fees, if you invest in a bond with compound interest, your investment will grow quicker than with simple interest. Why's that? You’ll earn returns on the money you’ve invested plus earnings from previous compounding periods. As a result, compound interest gives investments exponential growth.
• It’s free: Generally, with savings accounts, financial institutions include compound interest on assets at no extra charge. You won't need to pay an additional fee to apply compound interest to your account.
• Time is your friend: With savings, time is essential for compound interest to work, because the earlier you add money to your investment, the more compounding periods there will be. Remember, your initial investment amount and interest rate determine how profitable compounding interest will be. So, the longer you keep adding money to your account, the more you’ll see down the road.

Cons

Compound interest also has significant disadvantages.

• Fees are involved with investments: While compound interest costs nothing, investing always has fees. There are usually transaction costs, advisory fees, and ongoing expenses associated with investing in stocks and bonds. These fees will drain your investment account and slow its growth. Further, most interest income is taxable, so compound interest earnings will likely mean more taxation when you file.
• You’ll pay more than you borrowed: When it comes to loans, compound interest can be more harmful than good. This especially rings true when you’re paying compound interest instead of earning it. For instance, credit card debt with compounding interest can be financially ruinous because credit card issuers usually compound your interest daily.
• Patience is key: When investing with compound interest, time works in your favor. However, you won't see huge returns immediately, and you need substantial capital to reap significant benefits. As a result, compound interest requires time and discipline to be profitable.

The bottom line: Compounding interest makes loans more expensive

While compound interest can help you grow your money more with savings and investments, it makes loans and credit cards more costly. That's because compounding interest is added to the principal and to the accrued interest on past payments.

Getting your head around how compounding interest works, how it works differently in loans versus investments and savings, and the simple interest versus compound interest, will help you know the total cost of a loan.

If you're in the market for a mortgage, you can start your application today with Rocket Mortgage.