**Introduction**

Interest is mainly classified into two types:- One is the simple interest and the other is the compound interest. We will discuss the formulas for each type of interest to be able to solve problems on interest calculations.

**What Is Simple Interest?**

Interest is the fixed amount paid on borrowed money or received on lent money. The amount lent is called the Principal. The amount of the principal together with interest is called the Amount. When the amount of interest is calculated on the original principal for any given time period, it is known by the name simple interest.

**What Is Compound Interest?**

Compound interest on an a sum of money increases at a faster rate than simple interest. After the first interest period, the amount of interest is added to the principal amount and then the interest is calculated on the increased principal. The recent computed interest is added to the increased principal and then interest is computed again. This process continues over a certain number of compounding periods. The result is a much higher growth of the principal amount than simple interest would yield.

**Simple Interest and Compund Interest Formula **

**Simple Interest Formula:-**

I = P*r*t

Where: I = Simple Interest

P = Principal Amount

r = Rate of interest

t = Time period

**Compound Interest Formula:-**

I = [PV (1+i)n]-PV

Where: FV = Future value

PV = Present value

i = Rate of interest

n = Time period for compounding

**Solved Examples**

**A sum of Rs 2000 is borrowed and the rate is 10%. What is the simple and compound interest for 2 years?**

Calculation of Simple Interest

I = P*r*t

I = 2000*0.1*2

**I = 400**

Thus, the simple interest on the sum borrowed is Rs 400.

Calculation of Compound Interest

I = [PV (1+i)n]-PV

I = [2000 (1+0.1)2]-2000

I = (2000*1.21)-2000

I = 2420-2000=420

Thus, the compound interest on the sum borrowed is Rs 420.

**A sum of Rs 5000 is borrowed and the rate is 10%. What is the simple and compound interest for 2 years? (compounded half-yearly)**

Calculation of Simple Interest

I = P*r*t

I = 5000*0.1*2

**I = 1000**

Thus, the simple interest on the sum borrowed is Rs 1000.

Calculation of Compound Interest

I = [PV (1+i)n]-PV

I = [5000 (1+0.1)4]-5000

I = (5000*1.4641)-5000

I = 7320.5-5000=2320.5

Thus, the compound interest on the sum borrowed is Rs 2320.5.