# Simple Interest and Compound Interest- Basic concept and Shortcut tricks

Whenever we keep any amount on bank we are paid interest. The interest is usually specified as, say4% per annum. 4 % Per annum means if money invested is 100then interest is 4 % i.e. 4 Rs every year.

**Principal**: Which is denoted by P. The money lent for certain period is called principal.

**Amount**: Denoted by A, the final value of principal after the applicable growth i.e sum of principal and interest

**Rat of Interest**: Denoted by r, the percentage growth of principal or any single time period

**Interest**: Denoted by I, the mount by which a principal increase.

**Time period**: Denoted by t or n, time interval after which any interest is calculated.

**Simple Interest:** The interest in any time period is calculated as a percentage of initial amounts invested. Thus in simple interest, interest is always constant in any year.

**Simple Interest= P*r*t/100**

**Amount=P+ P*r*t/100**

**Amount=principal + interest**

**Example: **If r=10%, t=4 years then what is simple interest charged on a loan of Rs. 2000?

SI= P*r*t/100

SI= 2000*10*4/100

Rs.800

Shortcut Approach: For 4 years the interest payable would be equal to 10 x4=40 of principal. So 40% of 2000 which is Rs.800.

One can get any of p, r,t,SI if others are known just by putting simple values in above formula.

**Compound Interest**: In this type of interest, interest is calculated as percentage of amount outstanding at the start of time period not the initial investment. The amount outstanding is initial amount invested plus interest earned so far. Thus the interest earned is added to initial investment and new sum is considered as principal for next period.

**If P is principal kept at CI @r%, amount after n year will be P(1+r/100) ^{n}**

In the above problem if case was of compound interest then amount at the end of 4 year will be

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

A=2000(1+10/100)^{4}

2000*1.46

=Rs. 2928.2

So compound interest payable= 2828.2-2000

Rs. 928.2

**Conditions**:

Case 1: When interest is compounded annually,

Amount = P(1+r/100)^{n}

Case 2: When interest is compounded half yearly,

Amount = P(1+(r/2)/100)^{2n}

Case 3: When interest is compounded Quarterly,

Amount =P(1+(r/4)/100)^{4n}

When Rate of interest is r1%, r2%, and r3% for 1st, 2nd and 3rd year respectively.

Then,

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