SIMPLE INTEREST FORMULA

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In this lesson, we will learn about simple interest formula.

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Let's say that we have a loan of $5000, with an interest rate of 10% per year, and the loan duration is 3 years. Calculate the loan's simple interest.

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Now, the 'interest' is the amount of extra money we need to pay, for using the loan.

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Therefore, it is very important to learn how to calculate the interest of a loan. Here’s how.

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Since we are calculating simple interest, the amount of extra money we pay is the same every year.

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To show this, let's represent the principal, $5000, with this green bar. Now, after the 1st year, the interest is 10% of the principal, which is equals to $500.

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Here, how do we get this $500? To calculate it, we simply multiply $5000, with the interest 10%.

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10% is the same as, 10 over 100.

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By multiplying $5000 with 10 over 100, we will get $500. So, that is how we can calculate for the interest, $500.

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Next, after the second year, the interest is again 10% of the principal, which is another $500.

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Here, we can see that, the total interest for the first year and second year is $1000.

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Similarly, after the 3rd year, the interest is again 10% of the principal, which is another $500.

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Since this is a 3 year loan, the total interest that we need to pay is, $500 + $500 + $500, which is $1500.

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In other words, this is the total amount of extra money that we need to pay for using the loan.

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After understanding how simple interest works, let's derive the simple interest formula.

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First, let's change the principal to P, and the interest rate per year to r.

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By doing so, we can see that this $5000 becomes P, and this 10% becomes r.

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Now, P multiply with r, gives Pr.

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From here, we can see that this $500 can be represented with Pr. Therefore, we can represent each of these $500 as 'Pr'.

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Now, adding these terms together gives, 3Pr. Hence, we have, the interest I, equals to 3Pr. Let's rewrite it here.

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Notice that, the number 3 here, is actually the loan duration.

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So, when we change the loan duration to T years, we get, I = tPr. Next, we can shift this t back. By doing so, we get, I = Prt.

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With this, we have the simple interest formula, I = Prt.

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That is all for this lesson. Try out the practice question to further your understanding.

MATURITY VALUE FORMULA PART 2
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After understanding the basics behind simple interest, we can now learn about the maturity value formula.

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Consider a loan with the principal 'P', with interest rate per year of 'r'%, and the loan duration is 't' years.

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Derive the maturity value formula.

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Now, the maturity value is the total amount of money that we need to pay back, after the loan duration.

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To explain this, let's represent this green bar as the loan's Principal.

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And, represent the yellow bar as the loan's interest.

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Now, we can find the total amount of money to pay back, by adding the 'principal' together with the 'interest'.

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Knowing this, we can write the equation, maturity value, equals to principle, plus interest.

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Next, let’s represent the maturity value as S, principle as ‘P’ and interest as ‘I’.

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Now, from the previous lesson, we learn that the simple interest, I=Prt. Therefore, we can change this, I to Prt.

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Notice that, these 2 terms, have 'P' as a common factor.

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Hence, we can factorize these terms, by taking out ‘P’ in each term.

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By doing so, we get, P(1+rt).

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Finally, we have the formula for maturity value, S=P(1+rt).

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That is all for this lesson. Try out the practice question to further your understanding.