Compound interest

Definition, formula, how it’s calculated


  • Compound interest occurs when interest previously earned is added to the amount of principal invested or borrowed. It is commonly described as “interest earned on interest”.
  • Compound interest can work to your advantage as your investments grow over time, but against you if you are paying off debt, like credit cards.
  • If you are borrowing money, you want the interest to be compounded as little as possible; if you are investing, you want the interest to be compounded as often as possible.
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Warren Buffet once said that his wealth came from “a combination of living in America, certain lucky genes and compound interests.”

The billionaire investor meant that the interest earned on his investments had helped build his fortune. But Buffett also liked to warn people about the dangers of getting on the wrong side of the compound interest equation.

While compound interest is arguably the most important part of building wealth, it can also be one of the best ways to ruin your finances: To pay compound interest can cause debt to spiral out of control.

Most people only think of interest in terms of a high or low interest rate. But understanding how interest is calculated, or compounded, is also important. Knowing how compound interest works can help you avoid costly mistakes and get the most out of your money, whether you deposit it, invest it, borrow it, or spend it.

What is compound interest?

All interest is a percentage charged on, or earned by, a lump sum of money. Compound interest is a type of interest based on adding the original principal, that is, the original amount invested or borrowed, to the interest accrued from previous periods.

For example, let’s say you have $ 100 in a savings account and it earns interest at a rate of 10%, compounded annually. At the end of the first year, you would have $ 110 (100 in principal + 10 in interest). At the end of the second year, you would have $ 121 (110 in principal + 11 in interest). At the end of the third year, you would have $ 133.10 (121 in principal + 12.10 in interest). Etc.

In other words, with compound interest, you earn interest on the interest.

The revelation comes when you realize that compound interest grows capital exponentially, which means that as interest accumulates and the amount of money increases, the rate of growth becomes faster.

How fast your money grows depends on the interest rate and the frequency of funding. Interest can be compounded daily, monthly, quarterly, or annually, and the more frequently it is compounded, the faster it accumulates.

In the long run, the “magic of composition” can really add up. Here’s how an initial investment of $ 5,000 would increase if compounded semi-annually over 35 years, at an annualized interest rate of 5%:

If you are the one income money on interest, daily or monthly compounding is preferable to the year. On the other hand, if you are accused interest, monthly or annual compounding will save you money compared to the day-to-day.

Compound interest vs simple interest

While compound interest is “interest on interest” – calculated on both the principal amount and the accrued interest – simple interest is totally different. Simple interest is calculated alone on the balance of the initial capital or the deposit.

Let’s go back to our $ 100 savings account, but this time it pays 10% simple interest. This means that the 10% interest rate only applies to your initial principal of $ 100, so you earn $ 10 each year. Period. At the end of the first year, you would have $ 110. But at the end of the second year, you would have $ 120. At the end of the third year, $ 130 – compared to $ 133.10 in the compound interest account.

Even though we’ve used small numbers here, you can see how the farther you go, the more compound interest earns you – and the more it goes beyond simple interest.

Simple interest tends to be used in most student loans, mortgages, and installment loans – when you’re paying a store to purchase a major appliance over a period of time, for example.

How to calculate compound interest

Calculating compound interest sounds complicated, but it’s actually as easy as putting a few numbers in the right formula.

compound interest formula

The compound interest equation essentially adds 1 to the interest rate, increases that sum to the total number of compounded periods, and multiplies the result by the principal amount.

Shayanne Gal / Business Insider

Suppose you decide to deposit your annual bonus of $ 10,000 into a 5-year Certificate of Deposit (CD). You leave that money in the CD for the full five years and it earns an annual interest rate of 4% compounded daily. The numbers you would plug into each variable are:

  • P = $ 10,000
  • r = 0.04
  • n = 365
  • t = 5

The formula gives you $ 12,213.89 for A. This is the total amount of money you would have in your money market account after five years. This means that you have earned $ 2,213.89 in interest.

How Compound Interest Can Work Against You

As advantageous compound interest can be beneficial for savings, investments, and wealth building, it’s important to note that it can work against you if you pay off your debt. In fact, compounding is part of what makes an overdue credit card balance so deadly.

In fact, the above example could be reversed by imagining that you have a $ 10,000 balance on a credit card (we’ll assume that’s the same 4% compounded daily, even though the credit card APRs are usually much higher). You plan to put nothing else on the card and pay it off in five years. Even if you lower your balance and pay an extremely low interest rate, you could still end up paying a lot of interest charges – over $ 1,000 in fact.

And if you were to pay 18% compounded daily – which is closer to the average credit card interest rate – you would be paying $ 5,236 in interest after five years.

How to get the most out of compound interest

The best way to profit from compound interest is to save and invest.

Opt for a savings account that earns interest – like

high yield savings accounts

money market accounts
, and CD – is one way to play compound interest in your favor. When choosing an account, you’ll want to look for one with minimal fees and the highest annual percentage return (APY), which is the interest you can earn on your deposit over a 12-month period.

It should be noted that the interest rates even on the best savings accounts barely exceed inflation, so they are best for short-term savings. If you want to build long-term wealth, whether it’s saving for retirement or a goal for years to come, investing your money will really make it work for you.

Savings products offer interest rates that typically range from 0.01% to 3%, depending on the state of the economy, while the historical average rate of return in the stock market is 10%, before adjustment for inflation.

When opening an investment account like a 401 (k), IRA, brokerage account, or mutual fund, you have the option of automatically reinvesting any dividends or interest that your investments earn. This means that your returns will be compounded.

The financial report

Compound interest can be your friend or your foe, with the power to make you rich or to ruin you, depending on which side you find yourself on.

Fortunately, you don’t have to be a math genius to understand whether interest in an account will help or hurt you. If you’re borrowing money, you want the lowest possible interest rate, compounded as little as possible. If you’re investing money, the reverse applies: you not only want a good interest rate, but a rate that compounds early and often.

And when you compare loans, credit card APRs, savings account APYs, or the returns of other securities, check how often interest is accruing and make sure you’re comparing similar items. Two interest rates can be nominally the same, but if they compound at different rates it can make a big difference.

Whether it’s earning it or paying it off, the nature of compound interest means it’s exponentially better for your portfolio.