Compound Interest: Definition And Calculation

Interest rates can have a huge effect on what you earn in investments or repay on a loan. There’s often more to it than your rate, though, once you take compound interest into account. Depending on your situation, compound interest can either earn you or cost you money in the long run.

Let’s dig into the math behind compound interest and learn how it can affect the balance of your savings, debt and ultimately your personal finance health.

Compound interest, also called compounding interest, is what you earn on top of the principal amount of a loan or deposit, plus any accumulated interest. Interest is calculated at a designated interval and then added to the principal so that the next time interest is calculated, it’s against the sum of the principal plus any previously earned interest.

Say you put $100 in a savings account that earns 1% interest, compounded daily. On the first day, you’ll earn interest of one cent. On the second day, you’ll earn another 1% interest, only this time it will be 1% of $100.01. At the end of the first year, your account will contain $101.01. After Year 2, your account will contain $102.02. In Year 10, it will contain $110.52.

Simple Vs. Compound Interest

By contrast, without compounding, your account would contain $100.01 ($100 x 1% = one cent) after the first year. After Year 2, you would only earn another cent, bringing you to $100.02, because the interest is only calculated against the principal. This is called simple interest. After Year 10, the account would contain $100.10.

Simple interest is determined by the annual percentage rate (APR) of a loan or savings account, while the annual percentage yield (APY) accounts for compound interest.

Several key factors affect the outcome of your compound interest, some more so than others. Let’s take a look at these variables below.

• Your interest: The interest rate you’re charged for a loan or earn on an investment can have a big effect on your compound interest. A higher interest rate will generally raise the amount of interest you’ll earn or owe.
• Your initial principal: As with your interest, your principal amount in the beginning has a large impact on the calculation of your compound interest. How your interest compounds over time is based on your starting principal.
• The compounding frequency: It’s important to understand the rate at which your interest will compound when borrowing money or opening a savings account. Whether interest compounds daily, monthly or annually can determine how quickly the balance grows.
• How long you have the account or loan: A savings account can earn more interest the longer you keep it open, and a loan can likewise accrue more interest the longer you take to repay it.
• Your rate of repayment or deposit: How often you make deposits or loan payments has a big impact on your principal amount and your compound interest.

Examples Of Compound Interest

The following examples show how compound interest can affect different financial situations.

• Savings and checking accounts: Making deposits to an account that earns interest will help your balance grow over time, as the compound interest is added to the principal amount.
• Investment accounts: Depending on your investing risk tolerance, you can help your balance grow with time by investing and reinvesting. This can apply to stocks, certificates of deposit (CDs) and 401(k) accounts.
• Mortgages and other loans: Compound interest doesn’t usually work in your favor with personal loans, student loans or mortgages, because you’ll end up owing the accrued interest along with the amount you borrowed. This is why it’s best to pay your loan off early if possible.
• Credit cards: Credit card interest accrues every payment period, based on the balance you still owe. If you don’t charge anything to the card but pay off the interest every month, your balance should stay the same.

You can determine your compound interest by using an online compound interest calculator, or calculate it by hand with the formula below.

Compound Interest Formula

The compound interest formula is A = P (1 + r ∕ n)^(nt).

• A – Final amount
• P – Initial principal balance
• r – Annual interest rate
• n – Number of times interest is compounded per time period
• t – Number of time periods

Let’s imagine you had an average American credit card debt balance of $7,000 per household and your interest rate is 20%. Let’s also assume you move that amount to a balance transfer credit card that doesn’t require any interest payments for the first year, and you neither make payments nor charges to the account.

We’ll use the compound interest formula now to find what your balance would equal after the first year.

In this example, your calculations will look like this:

A = $7,000 (1 + .20 ∕ 365) ^ (365x1)

If you follow the standard order of operations, your equations should progress like this:

A = $7,000 (1.0005479452) ^ (365x1)

A = $7,000 (1.0005479452) ^ 365

A = $7,000 (1.2213358558)

A = $8,549.35 (after rounding off)

Compound interest can work both for and against you, depending on your situation. It makes building real wealth easier if you like saving money, but it can make repaying a loan more difficult if you’re in debt.

In our example at the beginning of the article, we saw how compound interest can increase the balance in your savings account through daily compounding over a number of years. This can be harmful to you when it comes to loans and credit cards, though.

If you’re a person with excellent credit, you’re probably charged an average credit card interest rate of about 16%. If your credit is average, it’s probably around 20%, and it’s probably around 23% if your credit is shaky. It’s a whopping average of around 26% if you take a cash advance, regardless of your credit. And those enormous interest rates are compounded daily.

Similarly with personal, student and other types of loans, the longer you take to pay them off, the more you’ll end up paying in interest. Mortgages will often compound daily, too.

You can take steps to get the most out of your compound interest. Try any of the following approaches to make your interest work for you.

• Give your accounts time to grow. If you start saving early enough, your compound interest can grow exponentially over the period of time you own the account.
• Make regular deposits into your accounts. Regular deposits into your savings accounts will increase the balances within, and with compound interest, leave you with even more later on.
• Check the compounding frequency. As mentioned, the rate at which your interest compounds can have a huge effect on what you earn – or owe – in interest.
• Pay down your debt quickly. Come up with a plan to pay off your debt in a short amount of time to avoid paying more in interest. Check first to see if your loan or mortgage has a prepayment penalty. If so, you could end up paying extra regardless.
• Compare different APYs. Calculate the APY of an account or a loan before committing to either. The APY, unlike APR, takes compound interest into consideration when determining the true cost of a loan or the rate of return on an investment.
• Consolidate your debt. Debt consolidation can be a handy tool for paying down your debt at a lower interest rate, lessening the effect compound interest can have on your loan. Consider applying for a personal loan to consolidate your debt.

Compound interest can reward or cost you in your financial ventures, depending on your situation. Keeping an interest-earning savings account open for many years will earn you a higher balance, while paying a loan off over a long period of time just creates more you have to pay back. Make compound interest work for you by understanding the math and knowing what you’re getting into before committing.

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