SIMPLE INTEREST

Simple interest

Simple interest is the additional amount of money we borrow or deposit certain amount of money after certain interval of time. It is calculated as I = $\frac{{{\rm{PTR}}}}{{100}}$

When the simple interest is added to the principal and the interest is taken from that money, it is called compound interest.

Some Important terms for the calculation of simple interest

Principal: It is the initial amount of money borrowed or deposited.

 P =$\frac{{{\rm{A*}}100}}{{100 + {\rm{TR\: }}}}$

P =$\frac{{100{\rm{*I}}}}{{{\rm{TR}}}}{\rm{\: }}$

Time: It is the intervalof time for which money is deposited or borrowed.

T =$\frac{{100{\rm{*I}}}}{{{\rm{PR}}}}{\rm{\: }}$

Rate: It is the interest on Rs 100 for 1 year .It is expressed in %.

R =$\frac{{100{\rm{*I}}}}{{{\rm{PT}}}}{\rm{\: }}$

Amount: It is the sum of principal and interest.

A = P + I

Examples

1. What sum of money deposited at 10% p.a wiil yield the same interest in 4 years as Rs 1680 yields in 5 years at 12 % p.a .

Soln

Principal (p₁ ) =Rs 1680

Time (T ₁ ) = 4years

Rate (R­₁ )=10%

I₁=$\frac{{{{\rm{P}}_1}{{\rm{T}}_1}{{\rm{R}}_1}}}{{100}}{\rm{\: }}$

= $\frac{{1680{\rm{*}}4{\rm{*}}10}}{{100}}$

 =Rs 672

Again,

Principal (p₂ ) =?

Time (T₂ ) = 5 years

Rate (R­₂ )=12%

p₂= $\frac{{{{\rm{I}}_2}{\rm{*}}100}}{{{{\rm{T}}_2}{{\rm{R}}_2}}}$

 = $\frac{{672{\rm{*}}100}}{{5{\rm{*}}12}}$

= 1120

2.

A sum of money amounts to Rs 1380 in 3 years and to Rs 1500 in 5 years .Find the sum and rate of interest.

Soln

Amount (A₁ ) = Rs 1380

Time (T₁ ) = 3years

Principal = Rs P

Rate = R %

P = $\frac{{{{\rm{A}}_1}{\rm{*}}100}}{{100 + {{\rm{T}}_1}{\rm{R}}}}$

 P = $\frac{{1380{\rm{*}}100}}{{100 + 3{\rm{*R}}}}$……………..i

Also,

Amount (A₂) = Rs 1500

Time (T₂) = 5 years

Principal = Rs P

Rate = R %

P = $\frac{{{{\rm{A}}_2}{\rm{*}}100}}{{100 + {{\rm{T}}_1}{\rm{R}}}}$

P =$\frac{{1500{\rm{*}}100}}{{100 + 5{\rm{*R}}}}$……………………..ii

From I and ii

We get

$\frac{{1380{\rm{*}}100}}{{100 + 3{\rm{*R}}}}$=$\frac{{1500{\rm{*}}100}}{{100 + 5{\rm{*R}}}}$

100+ 5R = 108 + 3.24R

R= 4.54%

3. Find simple interest on Rs. 10,000 for1$\frac{1}{2}$years at the rate of 5% per annum. Also find total amount.
Solution:
Let Principal = 10,000, Rate = 5% =5 /100 =0.05,

Time =$1\frac{1}{2}$ years =(1+$\frac{{1{\rm{\: }}}}{2}$)years =${\rm{\: }}\frac{3}{{{\rm{\: }}2}}$years 
I = $\frac{{{\rm{PTR}}}}{{100}}$

 =$10,000{\rm{*}}\frac{3}{2}{\rm{*}}0.05$

=750

Amount= Principal + Interest = 10000 + 750 =Rs 10750