# What Is Compound Interest? (With Formula and Examples)

By Indeed Editorial Team

Published 1 April 2022

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## What is compound interest?

If you're entering the financial industry, you might wonder, "What is compound interest?" Unlike simple interest, which refers to a specific percentage of money that you earn each year based on the original principal amount that you invested, compound interest is the interest a person makes based on the amount they've deposited and their previously earned interest.

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## Components of compound interest

To better understand compound interest, let's look at the components of compound interest. To calculate compound interest, you need three numbers:

### 1. Principal

The principle is the initial amount of money that you invest. For example, if your client deposits \$10,000 in the savings account, their principal is \$10,000. You can then help them calculate the first interest payment based on the amount of the principal. The greater the principal amount, the more they can receive in the future.

### 2. Interest rate

When they save money in a bank account or invest in a bond, the bank may pay your client extra money. The money a person earns on their investment is the interest. Interest rates refer to the proportion of the interest to the principal.

### 3. Compounding frequency

The compounding period is important for the calculation of compound interest. It's the number of times that the interest compounds per year. The greater the compounding frequency, the more interest a person can earn in the same period.

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## Benefits of compound interest

Compound interest can be beneficial if the person has the patience to allow their investment to grow. It helps people generate foreseeable profit from a relatively small investment over a long period. Compounding is comparable to the snowball effect because the principal and the interest earned compound together repeatedly. To demonstrate its powerfulness, here's an example:

If Tom saves \$50 per month for 10 years in a savings account, he can have \$6,000 after 10 years. Whereas, if he invests \$50 per month for 10 years and earns 10% compounded interest annually, he can have a final amount of \$10,080.

## How to calculate compound interest

Calculating the compound interest over a certain time involves applying the numbers into a basic mathematical formula. You can follow these steps to help your client calculate the compound interest efficiently and understand the concept:

### 1. Identify the numbers

Determine the interest rate, principal, compounding frequency and term period before you start your calculation. You can find this information on a bank's website or in the internal document about different investment plans. If you're investing for your client, you may also help them negotiate a better interest rate. Remember to ask about their budget and goals.

### 2. Calculate the final amount

Use the compound interest rate formula and replace each element with the actual number you have:

• A = P (1+r/n)nt

In this formula, A refers to the final amount, P means the principal, r is the interest rate, n indicates the compounding frequency and t refers to the number of years.

### 3. Calculate the compounded interest

After calculating the final amount, subtract the principal from the result. It's important to know the exact amount of interest instead of just the interest rate because it helps people make better comparisons between different investment plans. Calculate the compounded interest rate of each investment plan to make more informed investment decisions.

## Compound interest examples

To let you have a better understanding of how to apply the compound interest formula and how it looks like in real life, here are a couple of examples you can take reference from:

### Compound yearly interest calculation

Here's an example of an annual compound interest calculation:

Mr Chan invests part of his savings into an investment scheme. He deposits \$10,000 in a time deposit account in Best Bank Asia for five years. What is his final investment after five years if he can earn a return of 8% compounded interest annually?

In this example, P is \$10,000, r is 8%, n is one because it only compounds once per year and t is five because he invests his money for five years. Here's how the formula looks for this example:

• A = 10000 (1+0.08/1)1*5

After completing the calculation, we can see that Mr Chan can have a final amount of \$14,693 after five years. We then subtract the principal \$10,000 from the final amount, resulting in a compound interest of \$4,693.

### Compound biannual interest calculation

Here's an example of a biannual compound interest calculation:

Miss Fung receives \$10,000 from her grandparents as a graduation gift. She decides to invest the original \$10,000 for five years. We can find the value of the investment after the five years by calculating her final amount with 8% interest compounded every six months.

In this example, P is \$10,000, r is 8%, n is two because it compounds twice a year and t is five because she invests her money for five years. Here's how the formula looks for this example:

• A = 10000 (1+0.08/1)2*5

After completing the calculation, we can see that Miss Fung can earn \$14,802 after five years. We then subtract the principal \$10,000 from the final amount, resulting in a compound interest of \$4,802.

### Compound quarterly interest calculation

Here's an example of a quarterly compound interest calculation:

Miss Chan receives \$10,000 as her year-end bonus. She invests her entire bonus into a savings plan of Good Bank Asia for five years. What is her final investment after five years if she can earn a return of 8% compounded interest quarterly?

In this example, P is \$10,000, r is 8%, n is four because it compounds four times per year and t is five because she invests her money for five years. Here's how the formula looks for this example:

• A = 10000 (1+0.08/1)4*5

After completing the calculation, we can see that Miss Chan can earn \$14,859 after five years. We then subtract the principal \$10,000 from the final amount, resulting in a compound interest of \$4.859.

### Compound monthly interest calculation

Here's an example of a monthly compound interest calculation:

Mr Wong decides to open a flower shop. To fund his start-up, he makes an initial investment of \$10,000 for five years. What is the value of his investment after the five years if the investment earns a return of 8% compounded interest monthly?

In this example, P is \$10,000, r is 8%, n is 12 because it compounds 12 times per year and t is five because she invests his money for five years. Here's how the formula looks for this example:

• A = 10000 (1+0.05/1)12*5

After completing the calculation, we can see that Mr Wong can earn \$14,898 after five years. We then subtract the principal \$10,000 from the final amount, resulting in a compound interest of \$4,898.

If you want to help your clients to make decisions with compound interest, you can consider doing the following things:

### 1. Show them investment plans that have higher compounding frequencies

When you're helping your client open a savings account or compare between different investment plans, ask them to compare their compounding frequency. The more frequent the compounding period is, the more interest they can earn at the end of the period. Most investment plans in the market usually calculate interest monthly or annually.

### 2. Encourage them to invest longer

The effect of compounding is more dramatic when your clients invest money for an extended period. It's because the money compounds many more times. The earlier they begin investing, the more they can make on compound interest. You may encourage them to choose a plan that requires them to keep the money in the account for longer and explain the rationales behind it to them.

### 3. Ask them to consider the interest rate

The interest rate is the most determining factor in the final amount. The higher the interest rate, the faster your money can grow. Be careful when you're suggesting different plans for your clients. Make them aware that a high-interest rate may indicate a higher risk.

### 4. Advise them to invest more money at the beginning

You may encourage your client to deposit more money when they first start investing. Although the principal amount doesn't affect compounding, they can earn a higher interest during the first interest cycle. If they don't have much to start with, you can suggest plans that have higher interest rates, more compounding frequencies and longer investment periods.