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

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

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

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

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

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

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

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

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

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

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Adding 1, with 0.2, gives 1.2.

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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.

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2000 multiply with 1.728 gives, $3456.

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

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That is all for this example on calculate compound interest.

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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.

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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.

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Find the loan amount (principal), P.

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

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

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

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

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

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

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


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

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Let's write this down.

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Now we have, 1.21 = $1210.

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

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

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

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1210, divided by 1.21, gives $1000.

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

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That is all for this example.

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

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

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Find the interest rate, r.

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

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

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

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

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

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

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1452 two divided by 1200, gives 1.21.

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

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

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

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Square root of 1.21, gives 1.1.


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

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

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

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1.1 minus 1, gives 0.1.

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

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

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

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That is all for this example.