WTFinance: What is Compound Interest?

It’s claimed Albert Einstein once said “the power of compound interest is the most powerful force in the universe.” While it’s still unknown if he actually said this or not, the message remains powerful and widely adopted and here’s why: Compound interest is basically interest on the principal amount + interest that has already accrued. In other words, interest on interest. Compound interest is a unique concept because it can either work in your favor or against you, depending on how it is applied. Paying compound interest on a credit card, for example, could negatively impact your finances, while earning compound interest on savings can be beneficial.

Here, we’ll answer some key questions like, “what is compound interest?”, “how do you calculate compound interest?”, and more. Read on for a comprehensive overview, or use the links below to skip ahead to the section you’re most interested in.

• What is compound interest?
  • Examples of compound interest
• Compound interest vs. simple interest
• How does compound interest work?
• Compound interest formula
• Compound interest calculator
• Wrapping up

What is compound interest?

In the most basic sense, compound interest can be described as interest on interest. This added interest can apply to a high-interest savings account, bonds, stocks, or other kinds of securities—in this instance, compound interest serves as a benefit to you. But, compound interest can also cost you if it’s applied to debt, like a loan, for example. With these differences in mind, compound interest is the interest earned (or paid) on the principal, plus the accumulated simple interest you’ve earned (or paid) so far.

• Principal = amount borrowed or invested
• Interest rates =
  • Interest paid on principal
  • Interest paid on accrued interest
• Compounding schedule = interest can accrue daily, monthly, yearly or any other schedule laid out in the agreement.

Depending on whether you’re earning compound interest by saving money, investing, or paying it off on credit cards, loans, etc., compound interest can either help you out or hold you back.

Compound interest can apply to long-term investments, like high-yield savings accounts, as well as debts, like credit cards. In a savings account, compound interest would benefit you, as it would be paid out to you and ultimately, increase your total savings as it continues to build up. When applied to a line of credit, like an auto loan or credit card, compound interest may work against you as it increases the balance owed over time.

What is the purpose of compound interest?

Compound interest rewards investors, but the term “investors” can indicate a lot of different things. Banks, for example, benefit from compound interest when they lend money and then reinvest the interest into making more loans. When depositors receive interest on their bank accounts, bonds, or other investments, compound interest is also a benefit.

Examples of compound interest

As we’ve mentioned compound interest can have a positive or negative or negative impact on your finances. If you’re earning compound interest on savings, compound interest can increase your balance over time. Conversely, compounded interest on a line of credit can increase your total payment over the course of your loan. Let’s take a look at some examples to illustrate how compound interest can work for or against you, depending on the circumstance.

Example 1: Compound interest working in your favor:

Let’s say you deposit $1,000 into a savings account that pays 1% interest compounding annually. At the end of the first year, you would get $10 in interest, bringing the account balance to $1,010. Assuming you don’t make any deposits, at the end of the next year, you would earn 1% on the $1,010 in your account, earning $10.10 in interest at the 1% rate. At the end of the second year, your balance would be $1,020.10.

Though in this example the increase seems small, over time (and depending on the interest rate) you can see how the dollars can add up without much effort on your side. So take a look at the interest rate on the accounts you have now, and keep this in mind if you ever consider signing up with a new bank.

Example 2: Compound interest working against you:

Now, say you have a $5,000 credit card balance on a card that has an annual percentage rate (APR) of 15%, which compounds daily with a 30-day billing cycle. First you should calculate your daily interest rate from your purchase APR by dividing the 15% purchase APR by the number of days in a year. Then you multiply the daily rate by your average daily balance. Next: multiply that number by the number of days in your billing cycle to get your monthly interest charge.

In this case, your monthly interest amount is $63.70. Meaning, if you were to make payments of $63.70 every month to pay off the compound interest (and without spending any more on that card) your balance would never go up or down. However, by only paying the interest rate, you’re not making progress towards reducing the overall amount you owe on the card balance.

Compound interest vs. simple interest

Before we explain how compound interest works, let’s start with a basic overview of compound interest vs. simple interest.

Simple interest is measured on the principal balance alone, while compound interest is calculated on the principal balance as well as the compounded interest factored in to date. Compound interest, on the other hand, would increase the sum owed at a much faster rate than simple interest.

How does compound interest work?

Now, let’s take the foundation of simple interest to break down how compound interest works. After simple interest has factored into the balance you have or have to pay, compound interest is calculated on top of that amount. This means simple interest—the interest calculated on the principal balance—is included in the equation when you calculate compound interest.

The amount of compounding periods makes a big difference when calculating compound interest. The basic premise is that the more compounding periods there are, the more compound interest there is. When calculating compound interest, make sure you know how many compounding periods there are within your agreement.

Compound interest formula

Learning how to calculate compound interest can be helpful when evaluating investment opportunities or planning your debt repayment strategy. To estimate compound interest manually, you’ll need to have your principal amount,  nominal annual interest rate(%), and number of compounding terms handy.

Compound interest is computed by multiplying the initial principal amount by one and then multiplying the annual interest rate by the number of compound periods minus one. The principal amount is then deducted from the final value.

The compound interest formula is:

Compound Interest = Amount of Principle and Interest in Future (or Future Value) less Present Value

= [P (1 + i)n] – P

= P [(1 + i)n – 1]

P = principal, i = nominal annual interest rate in percentage, and n = number of compounding terms.

What about the Rule of 72?

The Rule of 72 is a simple, helpful rule for calculating the number of years it will take to double your money at a certain yearly rate of return. The formula used for the Rule of 72 is:

Years to Double Investment = 72/Interest Rate

Compound interest calculator

Calculating compound interest can be kind of complicated, especially when you’re looking for quick answers to assess an investment decision. Lucky for you, we’ve handled the heavy lifting by creating a compound interest calculator.

To use our calculator, you’ll need:

• Your starting investment amount
• The number of years you plan to accumulate (leave the amount untouched)
• Your typical contribution amount (weekly, bi-weekly, monthly, quarterly, or yearly)
• The rate of return on investment, as a percentage
• Compound interest frequency—is your interest compounded daily, monthly, semiannually, or annually?

Once you enter the information above, our compound interest calculator will generate a breakdown of your expected earnings over time.

Wrapping up

Put simply, compound interest is interest on your interest. Depending on the circumstances, compound interest can strengthen or set back your personal finance goals. Are you earning or paying compound interest? If you’re earning it, congrats – keep it up! If you’re paying it on credit cards, student loans, mortgages, etc. you can use our compound interest calculator, to see how much you’ll end up paying – and can adjust your budget accordingly.