Simple & Compounding Interest

Formula of Simple and Compounding Interest

 

Simple interest					Compounding interest
Year	Principal at the beginning of the year	Interest for the year	Interest till end of the year	Amount at end of the year	Principal at the beginning of the year	Interest for the year	Interest till end of the year	Amount at end of the year

 

Simple interest: when interest is calculated every year(or every time period) on the original principle. Then the sum of interest is called simple interest. Here interest of previous year is not considered as principle while calculating interest for next year.

p = principal amount

r = rate of interest, it is expressed as a percentage or decimal fraction.

n = time / period.

I = interest amount

A = sum of principal and interest

 

Then,

1. Simple interest : I = ( p x r x n) / 100
2. Total amount : A = { p + ( p x r x n) / 100}
3. Rate of interest : r ={(A-p) x 100/p x n %} ( if A, p and n given)
4. Time : n = {(A-p) x 100/p x r}
5. Principal amount : p = (A –i)

 

Compounding Interest :the previous year’s interest is added to the principle at the end of each period to arrive new principal for next period.

So previous year’s amount will be the principal of next year while calculating of compounding interest.

• So amount (A) will be after 2^nd year/ period or principle of 3^rd year (p) = {p( 1 + r/100)²}
• So amount (A) will be after 3^rd year/ period or principle of 4^thyear (p) = {p( 1 + r/100)³}
• So amount (A) will be after n year/ period ={ p( 1 + r/100)ⁿ}.
• The difference between the compounding interest for the n^th year and the n+1^thyear is equal to the interest for one year on the compound interest for the n^th year.