### How to Calculate Compound Interest #### Lesson Objective

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

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

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

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 #### Site-Search and Q&A Library

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