# Simple and Compound Interest - Atreya Roy

• Author: Atreya Roy is pursuing his BTech From Kalyani Government Engineering College, Bengal.

Value of money is never stagnant. It increases or decreases on various factors. This is called interest. Whenever you take a loan, you need to pay an extra amount with the amount of loan. This is called interest amount. It can be seen as the money you need to pay for the service you took from the lender. Today we will learn about interest

Interest are of two types :

1. Simple Interest : Money grows at a constant rate
2. Compound Interest : Principal amount changes after every time period

The formula for Simple Interest (SI) is  = P * R * T /100

Where  P = Principal amount on which interest is calculated

R = Rate of interest

T = Time in years

Amount = P + PRT/100 = Principal + Interest

The formula for Compound Amount

= P [1+(R/100)] ^n            [When money is compounded annually]

= P [1+(R/2*100)] ^2n       [When money is compounded half-yearly]

= P [1+(R/12*100)] ^12n   [When money is compounded monthly]

Note : The above formula will give us total amount. To get the Compound Interest only, we need to subtract the Principal from the Amount.

Note : Compound Interest > = Simple Interest

Example : A Certain amount of money becomes double in 4 years in Simple Interest. In how many years, will it becomes 3 times?

Solution :

Money gets doubled means, Interest  = Amount

So, P= P*R*4/100 Hence R= 25%

Now, Money becomes 3 times means Interest = 2P =P*25/100 *T

T= 8 years.

Hence after 8 years Money will be tripled

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