Formula for Compound Interest
Let’s derive the formula for compound interest by taking the previous example only, but this time we will not use the values for the variables.
[Tex]SI_{1} = \frac{P_{1} \times R}{100} [/Tex]
Now, the amount at the end of first year will the principal for the second year, i.e
[Tex]P_{2} = A_{1} = \frac{P_{1}R}{100} + P_{1} \\ \hspace{1.35cm} = P_{1}(1 + \frac{R}{100})[/Tex]
So, now SI for 2nd year
[Tex]SI_{2} = \frac{P_{2}R}{100}[/Tex]
Calculating the amount for the 2nd year,
[Tex]A_{2} = P_{2} + \frac{P_{2}R}{100} \\ \hspace{0.5cm} = P_{2}(1 + \frac{R}{100})[/Tex]
Now using the value of P2 in the above equation,
[Tex]A_{2} = P_{1}(1 + \frac{R}{100})(1+\frac{R}{100})\\ \hspace{0.5cm} = P_{1}(1 + \frac{R}{100})^{2}[/Tex]
Similar if we keep calculating for “n” years,
We’ll end up with this formula of amount
[Tex]A = P(1 + \frac{R}{100})^{n}[/Tex]
where P is the initial principal amount, R is the rate and n is the number of years after which the amount is calculated.
Compound Interest | Class 8 Maths
Compound Interest: Compounding is a process of re-investing the earnings in your principal to get an exponential return as the next growth is on a bigger principal, following this process of adding earnings to the principal. In this passage of time, the principal will grow exponentially and produce unusual returns.
Sometimes we come across some statements like “one year interest for FD in the bank @ 11 % per annum.” or “Savings account with interest @ 8% per annum”. When it comes to investment, there are usually two types of interests :
- Simple Interest
- Compound Interest
We already know about Simple Interest(S.I), we will look at Compound Interest(C.I) in detail in this article. First, let’s understand what is compounding through a story.
A Prisoner was once awaiting his death sentence when the king asked for his last wish.
The Prisoner demanded grain of rice (foolish demand right?) but added that the number of grain should be doubled after moving to every square till the last square of the Chess Board ( that is 1 on first, 2 on second, 4 on third, 8 on fourth, 16 on fifth and so on, till the 64th square).
The king thought that it is a very small demand and ordered his ministers to have that much amount of rice calculated and provided to the prisoner. The amount calculated was so big that the king lost his entire kingdom and was indebted to prisoner all of his life.
What the prisoner used was the idea of “Compounding“. Now, let’s define Compound Interest.
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