Compound Interest Formula
Lesson Objective
In this lesson, we will learn about the basics behind compound interest formula...
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About This Lesson
In this lesson, we will:
Learn about compound interest.
See how compound interest works.
(
1st math video
)
Find the formula for compound interest.
(
2nd math video
)
The
study tips
and
math videos
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 explain more on this formula. You can see the examples on using this formula
here
.
Math Video
Video on Figuring Compound Interest
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Video on Finding the Compound Interest Formula
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Math Video Transcript
COMPOUND INTEREST FORMULA PART 1 00:00:04.070 In this lesson, we will learn about the compound interest formula. 00:00:09.140 Consider a loan of $1000, with the compound interest rate of 10%, and the duration of the loan is 3 years. 00:00:18.000 Calculate the total amount of money that we need to pay back, after 3 years. 00:00:24.070 Before we learn about the compound interest formula, let's see how compound interest works. 00:00:31.030 Let's represent this green bar with the loan amount, $1000. 00:00:36.210 Now, after the first year, the interest will be 10% of the loan amount, $1000. 00:00:44.090 To calculate the interest, I, we multiply $1000, with the interest rate, 10%. 00:00:53.040 Now, before we can calculate, we need to change 10% to a decimal. 00:00:59.110 We can do so, by dividing 10% with 100. This gives 0.1. 00:01:07.240 $1000 multiply with 0.1, gives $100. 00:01:14.070 This is the amount of interest, after the first year. 00:01:18.160 Hence, we can find the amount of money that we owe after the first year, by adding $1000, with $100. 00:01:29.010 This gives $1100. Let's write this down here. 00:01:37.220 After the 2nd year, since the interest is compounding, the interest will be 10% of the current amount, $1100. 00:01:48.030 To calculate the interest, I, we multiply $1100 with 10%. 00:01:55.170 As calculated earlier, 10% converted to decimal is 0.1. $1100 multiply with 0.1, gives $110. 00:02:10.010 This is the loan's interest after the second year. 00:02:14.110 With this, we can find the amount of money that we owe after the 2nd year, by adding $1100, with $110. This gives $1210. Let's write this down here. 00:02:33.080 After the 3rd year, since the interest is compounding, the interest will be 10% of the current amount, $1210. 00:02:43.120 To calculate the interest, I, we multiply $1210, with 10%. 00:02:51.190 10% converted to a decimal is, 0.1. $1210 multiply with 0.1, gives $121. 00:03:05.200 Therefore, the interest is $121, after the 3rd year. 00:03:12.040 With this, we can find the total amount of money to pay back after 3 years, by adding $1210, with $121. 00:03:23.080 This gives, $1331. Let’s write it down here. 00:03:31.100 Hence, for a loan with compound interest, the total amount of money that we need to pay back after 3 years is, $1331. 00:03:43.220 In the second part, we will see how we can find the compound interest formula. PART 2 00:00:04.000 After understanding how compound interest works, let's find the compound interest formula. 00:00:11.040 Consider a loan of P dollars, with the compound interest rate of r%, and the loan duration is 3 years. 00:00:19.080 Find the total amount of money that we need to pay back, after 3 years. 00:00:25.110 Let's start by representing this green bar, with the loan amount, P. 00:00:31.230 Now, after the first year, the loan's interest will be r%, of P. 00:00:38.130 Hence, we can find the interest, I, by multiplying P, with r. 00:00:45.100 With this, we can find the amount of money that we owe, by adding P, with Pr. 00:00:53.040 This gives, P + Pr. 00:00:57.100 Notice that, these two terms have 'P' as a common factor. 00:01:03.100 Hence, we can factorize these 2 terms, by taking out 'P'. 00:01:09.200 By doing so, we have P(1+r). 00:01:15.110 So, this is the amount of money that we owe, after the first year. 00:01:21.180 Next, let's find out the interest at the end of 2nd year. 00:01:27.150 Before doing so, we let Q = P(1+r). Hence, this expression becomes Q. 00:01:39.180 Since this is a compound interest, the interest will be r%, of Q. 00:01:46.230 Hence, we can find the interest, I, by multiplying Q, with r. 00:01:53.240 Now, we can find the amount of money that we owe, by adding Q, with Qr. 00:02:01.060 By doing so, we have Q + Qr. 00:02:06.050 Again, notice that these 2 terms have 'Q' as a common factor. 00:02:12.050 Therefore, we can factorize these terms by taking out Q. This gives Q(1+r). 00:02:21.090 Let's change Q back to P(1+r). By doing so, we have P(1+r)(1+r). 00:02:34.100 Here, P(1+r)(1+r), gives (1+r)^2. 00:02:43.050 So, after the second year, the amount of money that we owe is, P(1+r)^2. 00:02:51.020 Here, we can see something interesting. 00:02:55.080 We know that, P(1+r) is the same as, P(1+r)^1. 00:03:04.140 Observe that, after the first year, we have P(1+r)^1. After the second year, we have P(1+r)^2. 00:03:20.050 From this, we can guess that, after the 3rd year, the amount money that we need to pay back is, P(1+r)^3. 00:03:31.120 Please verify this, to convince yourself. 00:03:35.180 Hence, if the loan duration is n year, we will have, P(1+r)^n. 00:03:45.090 Therefore, the total amount of money that we need to pay back after n years, A = P(1+r)^n. 00:03:56.000 This is the compound interest formula. 00:04:00.030 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 compound interest formula
or pick your choice of question below.
Question 1
on calculating the compound interest
Question 2
on using the compound interest formula
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