How to Calculate Compound Interest

What is compound interest?

Interest is the fee a lender will charge you for allowing you to use their money. Instead of just repaying the amount you borrowed, a charge is added to the balance. Lenders apply interest to installment loans, credit cards and other financial obligations. Banks also pay interest to people who deposit money at their institution because you are letting them use the money to make loans.

There are many ways that interest can be calculated, but the compound interest method is most often used for credit cards and bank deposit accounts. With it, interest accrues on the initial principal as well as the accumulated interest of a deposit or a debt.

By compounding interest, a principal amount can grow at a faster rate than if the simple interest method were applied. That’s because simple interest is based entirely on the percentage of the principal amount and not on any of the applied interest. This method is often used for car loans, term loans and some student loans.

Is this starting to sound complicated? In essence, compound interest works this way: Imagine depositing money into a savings account and leaving it there. The bank will first add interest to the amount you deposited. The next time the bank assesses interest, it will be on the amount you originally deposited plus the added interest. That means you are earning money on the principal plus what the bank has already given you.

For this reason, compounding interest on a savings account can help you build a nice nest egg with relatively little effort on your part.

The downside of compounding interest occurs when you owe money. For example, imagine you ran up a sizable bill on your business credit card. Instead of paying in full, you pay partially and move the remainder to the next month. The bank will add interest to that debt. If you continue to push that balance off, the next time interest is calculated, it will be on the balance that already grew with the interest that was added the prior month.

Therefore, compounding interest on a debt can add up quickly. The bank is charging you for the convenience of revolving the balance.

Simple interest vs. compound interest

To see how compound interest is calculated differently from simple interest, just do a side-by-side comparison with the same terms. Here is what it would be for each method, on $4,000, with an annual interest rate of 8% over the course of four years.

Simple interest example

Simple interest is calculated by multiplying the principal (P) by the rate (R) by time (T). This would be the calculation for the above example:

$4,000 x 0.08 x 4 = $1,280

So, in four years, the total interest would be $1,280 and the balance would grow to $5,280.

Compound interest example

Compound interest is calculated by applying the interest to the principal as well as the accrued interest, after each year. Breaking it down:

• After the first year, P x R x T (which, in this case, is 1) = $320, the new principal would be $4,320.
• At the end of the second year, P x R x T = $345.60, which is added to the old principal, creating a new principal of $4,665.60.
• At the end of the third year, P x R x T = $373.25, which, added to the old principal, is $5,038.85.
• Applying this formula again for the fourth year gives a new principal of $5,441.96, or with a total interest earned of $1,441.96.

Compared to the simple interest, the compound interest is $161.96 more.

Compound interest formula

The example above illustrates the concept of compound interest, but you can use another formula that is much simpler than calculating for each year and adding on. This is the formula:

P x (1+r)^t = Future value (FV)

In this formula, “P” represents present value, “r” represents the interest rate as a decimal, and “t” is the time period expressed as an exponent. This formula can also be used to work backward, which is useful when you want to establish a goal of saving a specific amount of money in a fixed time period. In other words, if you know your target FV and would like to figure out your needed present value, you can work the formula backward:

P = FV ÷ (1+r)^t

Components of compounding interest

When you want compounding interest to work in your favor because you are building funds for the future, keep the components of compounding interest in mind. For growing your money, you will want the following components.

• High interest rate: This should be the highest interest available and for which you can qualify. Deposit account rates are tied to the rates set by the Federal Reserve, though they do fluctuate based on the bank, so it’s best to shop around.
• High balance: You will also want to add to your balance so it grows, not just with interest but with regular deposits.
• Long time period: The longer you allow the funds to grow, the more compound interest will add to the principal. Through regular investments, a savings account can grow to quite a large amount. The younger you are when you start saving and contributing, the more time compounding can work to your benefit. While the results may seem slow at first, perseverance can really pay off. For example, a $5,000 annual contribution to an IRA for 45 years, with an average 8% return, can deliver retirement savings of more than $1.93 million, which is eight times the amount contributed.

The flip side of growing money, of course, is losing it. That’s easy to do when compounding interest is calculated on a debt. Again, keep the components of compounding interest in mind. This time, you will want the following components.

• Low interest rate: Seek out the credit product that has the lowest interest rate possible. While it’s best to keep debt to zero, if you do need or want to pay it off over time, a low interest rate is key.
• Low balance: Using a credit product that calculates interest with the compounding interest method can become an extraordinarily expensive endeavor when the balance is high. Make every attempt to charge only the amount you can afford to pay in full by the due date.
• Short time period: If you do have to pay a big balance in installments, make your payments as large as possible so you do not extend the date unnecessarily. A $5,000 credit card debt with a 25% interest rate that you pay over five years will cost you $3,805 in compounded interest. If you shortened the term to 12 months, the compounded would be $702.

Compound interest: A powerful friend or foe

In the end, compounding interest is a powerful way to either increase or decrease the value of your savings or debt. You have considerable control over this process. By calculating what you could earn with regular deposits, you can plan for your dreams, from starting your own business to retiring in luxury. And by calculating what you could lose by allowing a balance to accrue excessive interest, you can make better decisions when shopping and managing your accounts. The choice is yours.

Elaine J. Hom contributed to the writing and research in this article.