Question

What is the difference between the CI and SI on a sum of ₹1600 at 5% p.a for period of 2yr? Plz answer guys!!

Answer 1

Given :-

Sum = Rs. 1, 600

Rate of Interest = 5%

Time period = 2 years

Required to find :-

• Difference between the C.I. and S.I.

( C.I. stands for compound interest , S.I. stands for simple interest )

Formula used :-

$\boxed{ \tt{simple \: interest = \frac{PTR}{100} }}$

$\boxed{ \tt{A = P{ \bigg(1 + \frac{R}{100} \bigg ) }^{n} }}$

Here,

P - Principal

R - Rate of interest

T , n = Time period

A = amount

Solution :-

Given data ;

Principal = Rs. 1, 600

Time = 2 years

Rate of Interest = 5%

we need to find the difference between the simple interest & compound interest .

So,

Let's find the simple Interest ;

Using the formula ,

$\boxed{ \tt{simple \: interest = \frac{PTR}{100} }}$

$\tt{Simple \: interest = \dfrac{ 1, 600 \times 2 \times 5 }{100} }$

$\tt Simple \: Interest = 16 \times 2 \times 5$

$\tt Simple \: Interest = 32 \times 5$

$\tt Simple \: Interest = 160$

Similarly ;

Now,

Let's find the compound interest ;

$\boxed{ \tt{A = P{ \bigg(1 + \frac{R}{100} \bigg ) }^{n} }}$

$\tt A = {1, 600 \bigg( 1 + \dfrac{5}{100} \bigg) }^{2}$

$\tt{A = { 1, 600 \bigg( 1 + \dfrac{1}{20} \bigg) }^{2}}$

$\tt A = { 1, 600 \bigg( \dfrac{20 + 1}{20} \bigg) }^{2}$

$\tt A = { 1, 600 \bigg( \dfrac{21}{20} \bigg) }^{2}$

$\tt A = 1, 600 \times \dfrac{21}{20} \times \dfrac{21}{20}$

$\tt A = 16 \times \dfrac{21}{2} \times \dfrac{21}{2}$

$\tt A = \dfrac{16 \times 21 \times 21}{8}$

$\tt A = 2 \times 21 \times 21$

$\tt{ A = Rs. 882}$.

This implies ;

compound interest = Principal - Amount

compound interest = 1, 600 - 882

compound interest = 718

Hence,

Simple interest = Rs. 160

Compound interest = Rs. 718

So,

The difference between the S.I. and C.I. is ;

=> Rs. 718 - Rs. 160

=> Rs. 558

Therefore ;

The difference between the S.I. and C.I. = Rs. 558