# A 10-Year-Old’s Guide To Understanding Compound Interest

It’s not uncommon for corporate employees, especially those without technical degrees, to be unable to appreciate the concept of compound interest. But compound interest is amongst the most powerful forces in the universe, and its understanding is vital when it comes to managing you money, finances, or even your time. Here is a simple explainer:

The simplest definition of compound interest is the interest on a deposit or loan that is calculated both on the amount deposited/borrowed plus the previous interest. This means while calculating compound interest, you add up the previous interest earned to the initial principal amount. This is the reason why the compound interest you pay on a bank loan varies every year for the same principal amount.

Let’s look at an easy example to demonstrate how to calculate compound interest.

Suppose you borrowed \$50 from a friend and agreed to pay a 10% compound interest for one month. Now let’s calculate the interest and amount to be paid-

Compound interest for 1st month = 10% of \$50

= \$5

Total New Amount to be Paid After 1 Month = Borrowed Amount +
Compound Interest

= \$50 + \$5

= \$55

However, you failed to pay him the entire amount after one month, so the interest will now accumulate and be calculated as below:

Compound interest for 2nd month = 10% of New Amount

= 10% of \$55

= \$5.5

Total Amount to be paid after 2 months = Total amount after 1 month +
Compound Interest of 2nd month

= \$55 + \$5.5

= \$60.5

Similarly, there are numerous examples to understand how compound interest works. The best way is to learn about its importance in everyday life. Keep reading to find out.

Why Is Compound Interest so Important for Students?

To our surprise, compound interest is not only associated with mathematics or bank loans but also with other natural phenomena like:

1. The growth rate of bacteria.
2. The increase in the size of the animal population.
3. The rise or depreciation in the value of your father’s car.

Learning about compound interest helps us understand how such natural things multiply and accumulate over time.

However, there are more reasons to enjoy studying compound interest or CI, here are a few of them-

1. Strengthens Everyday Mathematic Skills

The most important reason to study compound interest is to sharpen the everyday mathematical skills. From money to percentages to profit and loss, compound interest envelopes critical mathematical topics that enable people to understand commercial math easily. Mastering compound interest will help you excel at complex topics like loans, asset valuation, and taxes in the longer run.

1. Money Grows Faster With CI

With simple interest, your principal amount remains unchanged and hence, you earn the same amount every month or year. In contrast, compound interest earns you interest on interest already earned. So, the next time you visit a bank, ask them why a certain deposit with compound interest is earning you more than the one with simple interest.

1. CI Explains the Power of Small Values and Time

Earning \$5 every month may not feel magnificent. But if you teach children how \$5 + \$5 + \$5… up till 12 months will sum up to a grand \$60, this will surely raise their eyebrows. Compound interest is important for students because it teaches them how small values, when invested for a long time, can give better returns. You may apply the same logic to exercising daily or brushing teeth twice every day.

What Is the Rate of Return in Compound Interest?

So far, you have only read about the interest rate used while calculating simple or compound interests. However, there’s another important term called ‘rate of return’. This term is specifically applied when we invest our money or assets in return for a certain amount of interest or value over a period.

The rate of return is the profit earned on any given investment. It is expressed as a percentage of the initial investment. When compounded annually, the rate of return is often termed as “Compound Annual Growth Rate” or CAGR

That’s where a rate of return is different from an interest rate. An interest rate is always paid on a loan or borrowings while a rate of return is the earned profit (or loss) on any given investment.

For students, it is important to note that exam questions around a compound rate of return can appear like:

1. Calculate the profit on an investment of \$300 promising a 10% compound rate of return for 2 years.
2. What is the compound rate of return for an investment that earned you \$400 over an initial amount of \$1000?

How to Calculate Rate of Return in Compound Interest?

We will take up the first question to help students understand how the compound rate of return works.

Suppose you invested \$300 that offers a 10% compound rate of return for 2 years.

Now, instead of carrying out the long-form method of compound interest as demonstrated in the first example, let’s discover a new formula:

CI = P ( 1 + R/100)T

Here, P = Principal Amount

R = Rate of interest/ return

T = Time period

CI = Compound Interest

Let’s fill in the figures from the above question into the formula-

CI = \$300 ( 1 + 10/100 )2

= \$300 ( 1 + 1/10 )2

= \$300 (110/100)2

= \$3 X 11 X 11

= \$363

So, the total amount that your investment would earn you after 2 years = \$363.

Now, you can easily calculate the profit that you earned. Simply deduct the initial investment amount from the amount earned after the compound rate of return applied. To demonstrate-

Profit earned = Total amount earned after 2 years – Initial investment

= \$363 – \$300

= \$63

So, a compound rate of return of 10% on an investment made of \$300 for 2 years will land you with a profit of \$63.

Similarly, we can use the CI formula to calculate the rate, time, or principal amount depending upon the question asked. What’s important is to understand how the rate of return can affect compound interest and vice versa. Here’s how the tutors at CueMaths explain the significance of the rate of return to students.

Importance of Rate of Return in Compound Interest

In the banking and financial sector, the compound rate of return is considered more accurate than average or semi-annual interest rates. It is because CAGR tells us the actual performance of an investment over a period of time.

More so, there are several reasons why the rate of return matters when it comes to compound interest. The most crucial reasons to apply a rate of return includes-

1. The Cumulative Effect

Similar to compound interest, a compound rate of return also represents the money earned on money accumulated. Over a period of time, a compound rate of return is the best form of interest that you can earn over an investment. Unlike simple interest, CAGR multiplies money and interest amounts together to give higher returns.

1. Standard Variable to Evaluate Investments

A compound rate of return has become a standard and universally accepted rate to calculate the profitability of any asset or investment. Learning the basics of the rate of return will help them compare different investment plans easily and make a well-informed decision.