Simple Interest Formula
Lesson Objective
In this lesson, we will learn about the simple interest formula and the maturity value formula...
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About This Lesson
In this lesson, we will:
Learn about the basics behind simple interest.
See the steps to derive the simple interest formula.
(
1st math video
).
See the steps to derive the maturity value formula.
(
2nd math video
).
The
study tips
and
math videos
below will explain more.
Study Tips
Tip #1
The formula for finding the simple interest,
I
is given below:
Where:
P
is the principal (the amount of money borrowed)
r
is the interest rate (per year or per annum)
t
is the loan duration in years.
Tip #2
The formula to find the maturity value,
S
is given below:
Where the definition for
P
,
r
and
t
are the same as above.
The math videos below will explain the basics and the steps to derive these two formulas. You can see the examples on using these formulas
here
.
Math Video
Video on Simple Interest Formula
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Video on Maturity Value Formula
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Math Video Transcript
SIMPLE INTEREST FORMULA 00:00:04.170 In this lesson, we will learn about simple interest formula. 00:00:09.200 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. 00:00:23.120 Now, the 'interest' is the amount of extra money we need to pay, for using the loan. 00:00:29.230 Therefore, it is very important to learn how to calculate the interest of a loan. Here’s how. 00:00:36.180 Since we are calculating simple interest, the amount of extra money we pay is the same every year. 00:00:43.210 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. 00:01:00.070 Here, how do we get this $500? To calculate it, we simply multiply $5000, with the interest 10%. 00:01:10.120 10% is the same as, 10 over 100. 00:01:16.060 By multiplying $5000 with 10 over 100, we will get $500. So, that is how we can calculate for the interest, $500. 00:01:16.060 Next, after the second year, the interest is again 10% of the principal, which is another $500. 00:01:39.060 Here, we can see that, the total interest for the first year and second year is $1000. 00:01:47.090 Similarly, after the 3rd year, the interest is again 10% of the principal, which is another $500. 00:01:56.070 Since this is a 3 year loan, the total interest that we need to pay is, $500 + $500 + $500, which is $1500. 00:02:07.200 In other words, this is the total amount of extra money that we need to pay for using the loan. 00:02:15.110 After understanding how simple interest works, let's derive the simple interest formula. 00:02:22.140 First, let's change the principal to P, and the interest rate per year to r. 00:02:30.100 By doing so, we can see that this $5000 becomes P, and this 10% becomes r. 00:02:38.240 Now, P multiply with r, gives Pr. 00:02:44.000 From here, we can see that this $500 can be represented with Pr. Therefore, we can represent each of these $500 as 'Pr'. 00:02:56.200 Now, adding these terms together gives, 3Pr. Hence, we have, the interest I, equals to 3Pr. Let's rewrite it here. 00:03:11.050 Notice that, the number 3 here, is actually the loan duration. 00:03:16.240 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. 00:03:32.180 With this, we have the simple interest formula, I = Prt. 00:03:39.240 That is all for this lesson. Try out the practice question to further your understanding. MATURITY VALUE FORMULA PART 2 00:00:03.210 After understanding the basics behind simple interest, we can now learn about the maturity value formula. 00:00:11.190 Consider a loan with the principal 'P', with interest rate per year of 'r'%, and the loan duration is 't' years. 00:00:20.130 Derive the maturity value formula. 00:00:24.140 Now, the maturity value is the total amount of money that we need to pay back, after the loan duration. 00:00:31.240 To explain this, let's represent this green bar as the loan's Principal. 00:00:37.190 And, represent the yellow bar as the loan's interest. 00:00:42.190 Now, we can find the total amount of money to pay back, by adding the 'principal' together with the 'interest'. 00:00:51.240 Knowing this, we can write the equation, maturity value, equals to principle, plus interest. 00:00:59.230 Next, let’s represent the maturity value as S, principle as ‘P’ and interest as ‘I’. 00:01:08.210 Now, from the previous lesson, we learn that the simple interest, I=Prt. Therefore, we can change this, I to Prt. 00:01:23.060 Notice that, these 2 terms, have 'P' as a common factor. 00:01:29.060 Hence, we can factorize these terms, by taking out ‘P’ in each term. 00:01:35.240 By doing so, we get, P(1+rt). 00:01:42.060 Finally, we have the formula for maturity value, S=P(1+rt). 00:01:50.200 That is all for this lesson. Try out the practice question to further your understanding.
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 simple interest formula
or pick your choice of question below.
Question 1
on the using the simple interest formula
Question 2
on using the maturity value formula
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Q&A Library
. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.
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