# How Does Compound Interest Work?

Compound interest is interest that applies to both the principal amount and any interest that has accrued over previous periods of time. The interest will grow much faster on a loan or deposit when it is compounded compared to simple interest, which only applies to the principal amount. The rate of growth is determined by the frequency of compounding, or the number of compounding periods. The higher the compounding frequency, the faster the interest will grow. Interest can be compounded daily, weekly, monthly, quarterly, semi-annually, or annually.

You can accrue compound interest on a debt or deposit. When compound interest accrues on a loan, the amount of money you owe will grow at an increasingly rapid rate. If compound interest applies to your deposit, your savings will grow at an increasingly rapid rate.

## What is compound interest?

Compound interest is often referred to as interest on interest. Almost all loans and deposits grow at a set interest rate. With compound interest, the rate applies to the principal amount and any interest that has already accrued. Once the interest compounds, any interest that has accrued gets added to the principal. The interest rate then applies to the principal plus the added interest.

The compound frequency is one of the most important factors when calculating compound interest. The more often the interest gets compounded, the faster the interest will accrue.

For example, a loan or deposit of \$100 will grow much faster with an interest rate of 5% that’s compounded semi-annually compared to \$100 with an interest rate of 10% that’s compounded annually.

Let’s start the first \$100 with a 5% interest rate. If the interest is compounded semi-annually, the \$100 will grow to \$105 after six months. The 5% interest rate will then apply to the new total of \$105. At the end of the year, the loan or deposit will now be worth a total of \$110.25.

The second \$100 has a higher interest rate but it only gets compounded once a year. At the end of the year, the second \$100 will only grow to \$110.

The difference gets more pronounced as time goes on.

As important as the compounding frequency can be, there can be some variations in terms of when the accrued interest actually gets credited to your account. For example, interest may get compounded daily, but it only gets added to the principal at the end of the month. You will only accrue compound interest when the previous interest is credited to the principal amount.

Some banks and lenders also offer what’s known as continuously compounding interest, which means that interest gets compounded at every possible instant, but on a practical level, compounding interest continuously isn’t that different from a daily compounding schedule.

## The Formula for Annual Compound Interest

You can use the following equation for compounding interest:

Compound Interest = P [(1 + i)– 1]

“P” is the principal amount, “i” is the nominal annual interest rate in percentage terms, and “n” is the number of compounding periods.

The compound interest on a three-year loan of \$10,000 with a rate of 5% that’s compounded annually would be:

\$10,000 [(1 + 0.05)3 – 1] = \$10,000 [1.157625 – 1]

This comes out to \$1,576.25 in compound interest after three years.

Conversely, the formula for compounded monthly interest would be:

Compounded Interest =  P(1 + (r/12) )12t – P

In this case, “t” stands for the overall tenure or time period or number of years. The interest gets compounded 12 times a year or at the end of each month. The annual interest rate “r” gets divided by 12, and the time period is multiplied 12 times.

For example, a loan of \$10,000 with an annual interest rate of 8% that compounds monthly would be:

10,000(1 + (0.08/12) )12 – 10,000 = \$829.13 after one year. After two years, the compound interest would grow to \$1,728.88.

## How Compound Interest Applies to Loans

Compound interest can be a serious problem if you are in debt. The higher the number of compounding periods, the faster interest will accrue. If interest is being compounded on your loan, it’s best to pay it off as soon as possible. If you are looking for a loan, consider finding one with a low compound frequency to avoid paying more in interest.

The lender will provide a compounding schedule. Most credit cards, mortgages, car, personal, and business loans come with a monthly compound frequency.

## How to Compound Money

Compound interest can also work in your favor if you have savings deposited in an account that accrues interest. You can increase your savings by finding an account that offers compound interest instead of basic interest. The more frequent the compounding period, the faster your savings will grow. The growth may be small at first, but the rate of growth will continue to increase over time.

Your bank will offer a certain compounding schedule, which shows you how often the interest will be compounded.

Most banks use a daily compounding schedule on savings accounts. The same is usually true of money market accounts. Certificates of deposit often have a wide range of compounding frequencies, ranging from daily to semi-annually.

Focusing on just the interest rate may not tell you everything you need to know. Consider going with a lower interest rate if it comes with a higher number of compounding periods. Calculate the compound interest ahead of time to see how much you stand to earn in the future. If you are calculating compound interest on a long-term investment, holding onto it for 20 years or 30 years can help triple if not quadruple your savings.

Use compound interest to accumulate savings faster. Your money will grow at an ever-increasing rate. The longer you keep your deposit in the bank, the more interest will accrue.

Investors will often calculate future compound interest to analyze their estimated rate of return. 