### How to Calculate Compound Interest

#### Lesson Objective

In this lesson, we will see some examples on how to calculate compound interest...

#### About This Lesson

We will be using some examples to show how to use the compound interest formula. These examples will be on:

- Calculating the total amount A, when the P, r and n are given. (1st math video)
- Calculating the principal P, when the A, r and n are given. (2nd math video)
- Calculating the interest rate r, when A, P and n are given. (3rd math video)

The study tips and math video below will explain more.

### Study Tips

#### Tip #1

The compound interest formula is given below:

Where:

- A is the total amount of money (including interest) after n years
- P is the principal (the amount money borrowed or invested)
- r is the interest rate (per year or per annum)
- n is the loan or investment duration in years

The math videos below will show how to calculate compound interest and more...

### Math Video

#### Video on calculating for A when P, r and n are given...

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#### Math Video Transcript

00:00:03.230

In this example, we will learn how to calculate compound interest.

00:00:09.230

Consider a loan of $2000 with the compound interest rate of 20% and the duration of the loan is 3 years.

00:00:19.200

Find the total amount of money that we need to pay back, after 3 years.

00:00:26.040

Now, we start with the compound interest formula, A=P(1+r)^n

00:00:34.030

Where, 'A' is the total amount. 'P' is the loan amount, or principal. 'R' is the interest rate. And 'N' is the loan duration.

00:00:48.030

Here's how we calculate compound interest. Since the principal is given as $2000. We can substitute P, with 2000.

00:00:55.190

Now, the interest rate is given as 20%. Hence, we can substitute 'R', with 20%.

00:01:06.040

The loan duration is given as 3 years. Therefore, we can substitute 'N' with 3..

00:01:14.130

Note that, before we can calculate compound interest, we need to convert 20% to a decimal.

00:01:21.160

We can do so, by dividing 20%, with 100. This gives 0.2.

00:01:33.220

Adding 1, with 0.2, gives 1.2.

00:01:39.110

Next, 1.2 to the power of 3 is the same as, 1.2 x 1.2 x 1.2. This gives 1.728. Let’s write this down here.

00:01:55.150

2000 multiply with 1.728 gives, $3456.

00:02:03.130

Hence, the total amount of money that we need to pay back after 3 years is, $3456.

00:02:14.000

That is all for this example on calculate compound interest.

#### Video on calculating for P when A, r and n are given...

#### Math Video Transcript

00:00:04.070

After learning how to calculate compound interst, we will now see how we can find the principal of a loan, using the compound interest formula.

00:00:12.210

Consider a loan with the compound interest rate of 10%. The duration of the loan is 2 years. And the total amount of money that we need to pay back after 2 years is $1210.

00:00:28.020

Find the loan amount (principal), P.

00:00:32.020

Now, we start with the compound interest formula, A=P(1+R)^n.

00:00:40.130

Since the total amount of money that we need to pay back is given as $1210, we can substitute 'A' with 1210.

00:00:51.220

The interest rate is given as 10%. Hence, we can substitute 'R' with 10%.

00:01:01.130

Next, the loan duration is given as 2 years. Hence, we can substitute 'N' with 2.

00:01:11.080

Now, before we can calculate, we need to change 10% into a decimal.

00:01:17.170

To do so, we divide 10% with 100. This gives 0.1.

00:01:27.090

Let's calculate. Adding 1 with 0.10, gives 1.1.

00:01:35.200

Next, 1.1 square is the same as, 1.1 multiply with 1.1. This gives 1.21.

00:01:47.020

Let's write this down.

00:01:50.100

Now we have, 1.21 = $1210.

00:01:58.190

Let's rewrite this equation, so that it looks neater.

00:02:03.160

To find 'P', we need to remove 1.21. We can do so, by dividing both sides of the equation with 1.21.

00:02:15.090

By doing so, we have, P=1210/1.21.

00:02:24.170

1210, divided by 1.21, gives $1000.

00:02:32.140

Hence, the principal of this loan, P, is $1000.

00:02:40.040

That is all for this example.

#### Video on calculating for r when A, P and n are given...

#### Math Video Transcript

00:00:04.170

In this example, we will learn how to find the interest rate of a loan, using the compound interest formula.

00:00:13.040

Consider a loan of $1200. After 2 years, the total amount of money that we need to pay back is $1452.

00:00:24.190

Find the interest rate, r.

00:00:28.170

Now, we start with the compound interest formula, A=P(1+r)^n.

00:00:38.100

Since the total amount is given as $1452, we can substitute 'A' with 1452.

00:00:48.020

Since the principal is given as $1200, we can substitute 'P' with 1200.

00:00:56.230

The duration of the loan is 2 years. Therefore, we can substitute 'N' with 2.

00:01:04.130

Let's solve for 'R'. First, we need to remove 1200. To do so, we divide both sides of the equation, with 1200.

00:01:19.090

This gives. 1452/1200 = (1+r)^2.

00:01:30.140

1452 two divided by 1200, gives 1.21.

00:01:38.230

Now we have, (1+r)^2 = 1.21. Let's rewrite it here.

00:01:49.220

Next, we need to remove this 'square'. To do so, we square root both sides of the equation.

00:01:58.190

By doing so, we get, 1 + R = 1.121.

00:02:09.050

Square root of 1.21, gives 1.1.

00:02:15.010

Now, we have 1 + r = 1.1. Let's rewrite it here.

00:02:24.120

Finally, to get 'r', we need to remove 1. We can do so, by adding both sides of the equation with -1.

00:02:36.050

By doing so, we have, r = 1.1 -1.

00:02:44.040

1.1 minus 1, gives 0.1.

00:02:49.070

Now, we need to convert this decimal, 0.1, to percent.

00:02:55.110

To do so, we simply multiply 0.1, with 100. This gives 10%.

00:03:07.060

Hence, the interest rate of this loan, 'r', is 10%.

00:03:15.020

That is all for this example.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on calculate compound interest or pick your choice of question below.

- Question 1 on using how to calculate compound interest
- Question 2 on finding the principal of a loan using the compound interest formula

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