Hello Aspirants, Today we will deal with Compound Interest - Important Terms, Formulas and Shortcuts you should know to solve questions based on this topic in any competitive exams.

Now, Let's start the lesson !

When the interest is applied to original principal as well as the interest earned on that principal, then the interest is said to be compound interest.

If we have taken loan of Rs X and the compound interest applies to it, then

For 1st year, Compound Interest will be same as Simple Interest. Let it be Y

From 2nd Year, Compound Interest will be calculated on original Principal ( X ) as well as interest earned on that principal in 1st Year ( Y ) and so on...

So, we can conclude that Amount at the end of 1st year will become the principal for the 2nd year and Amount at the end of 2nd year becomes the Principal of 3rd year and so on...

Amount = Principal + Interest

A = P (1+r/100) ^n

Compound Interest = [P (1+r/100) ^ n - P] = P [(1+r/100) ^ n – 1]

Here, A= Amount, P= Principal, r= Rate of Interest % and n= no. of years

When interest is compounded annually

Amount = P (1+r/100) ^n and Compound Interest = P [(1+r/100) ^ n –1]

When interest is compounded half - yearly

Amount = P (1+r/200)^2n and Compound Interest = P [(1+r/200)^2n - 1]

When interest is compounded quarterly

Amount = P (1+r/400)^4n and Compound Interest = P [(1+r/400)^4n - 1]

When interest is compounded monthly

Amount = P (1+r/1200)^12n and Compound Interest = P [(1+r/1200)^12n - 1]

When interest is compounded for a fraction of years suppose say 4 whole 2/5 year

Amount = P(1+r/100)^3×(1+(2r/5)/100)

Note : Here, A= Amount, P= Principal, r= Rate of Interest % and n= no. of years

When Rates of Interest are different for different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively, Then

Amount = P(1+r1/100)×(1+r2/100)×(1+r3/100)

Now, Let's start the lesson !

**What is Compound Interest ?**When the interest is applied to original principal as well as the interest earned on that principal, then the interest is said to be compound interest.

**Let's understand with an example :**If we have taken loan of Rs X and the compound interest applies to it, then

For 1st year, Compound Interest will be same as Simple Interest. Let it be Y

From 2nd Year, Compound Interest will be calculated on original Principal ( X ) as well as interest earned on that principal in 1st Year ( Y ) and so on...

So, we can conclude that Amount at the end of 1st year will become the principal for the 2nd year and Amount at the end of 2nd year becomes the Principal of 3rd year and so on...

**Some Basic Compound Interest Formula :**Amount = Principal + Interest

A = P (1+r/100) ^n

Compound Interest = [P (1+r/100) ^ n - P] = P [(1+r/100) ^ n – 1]

Here, A= Amount, P= Principal, r= Rate of Interest % and n= no. of years

**Some important cases for calculating Compound Interest :**When interest is compounded annually

Amount = P (1+r/100) ^n and Compound Interest = P [(1+r/100) ^ n –1]

When interest is compounded half - yearly

Amount = P (1+r/200)^2n and Compound Interest = P [(1+r/200)^2n - 1]

When interest is compounded quarterly

Amount = P (1+r/400)^4n and Compound Interest = P [(1+r/400)^4n - 1]

When interest is compounded monthly

Amount = P (1+r/1200)^12n and Compound Interest = P [(1+r/1200)^12n - 1]

When interest is compounded for a fraction of years suppose say 4 whole 2/5 year

Amount = P(1+r/100)^3×(1+(2r/5)/100)

Note : Here, A= Amount, P= Principal, r= Rate of Interest % and n= no. of years

When Rates of Interest are different for different years, say r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively, Then

Amount = P(1+r1/100)×(1+r2/100)×(1+r3/100)

**Some more cases on types of questions asked in competitive exams :**

- If a sum of money becomes n times in x years and m times in y years then n^1/x = m^1/y

**Some Shortcuts used to solve Questions :**

- Relationship between Compound Interest and Simple Interest for 2 Years

CI/SI = ( 200 + r ) / 200

- Difference between Compound Interest and Simple Interest for a sum of money at r % for 2 Years

Difference = P ( r / 100 )^2

- Difference between Compound Interest and Simple Interest for a sum of money at r % for 3 Years

Difference = Pr

^{2}( 300 + r ) / 100^{3}
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