Question

Find the difference between the compound interest and the simple interest on Rs. 30000 in 2 years at 8% per annum.​

Answer 1

$\large\underline{\sf{Solution-}}$

Case :- 1 Compound interest

Principal, P = Rs 30000

Rate of interest, r = 8 % per annum compounded annually.

Time, n = 2 years

We know, Compound interest (CI) on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

$\boxed{ \rm{ \:CI \: = \: P\bigg[1 + \dfrac{r}{100} \bigg]^{n} \: - \: P \: \: }}$

So, on substituting the values, we get

$\rm \: CI \: = \: 30000 {\bigg[1 + \dfrac{8}{100} \bigg]}^{2} - 30000$

$\rm \: CI \: = \: 30000 {\bigg[\dfrac{100 + 8}{100} \bigg]}^{2} - 30000$

$\rm \: CI \: = \: 30000 {\bigg[\dfrac{108}{100} \bigg]}^{2} - 30000$

$\rm \: CI \: = \: 30000 \times \dfrac{108}{100} \times \dfrac{108}{100} - 30000$

$\rm \: CI \: = \: 3 \times 108 \times 108 - 30000$

$\rm \: CI \: = \: 34992 - 30000$

$\rm\implies \:\boxed{ \rm{ \:CI \: = \: Rs \: 4992 \: \: }}$

Case :- 2 Simple interest

Principal, P = Rs 30000

Rate of interest, r = 8 % per annum.

Time, n = 2 years

We know, Simple interest (SI) on a certain sum of money of Rs P invested at the rate of r % per annum for n years is given by

$\boxed{ \rm{ \:SI \: = \: \frac{P \times r \times n}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: SI \: = \: \dfrac{30000 \times 8 \times 2}{100}$

$\rm \: SI \: = \: 300 \times 8 \times 2$

$\rm\implies \:\boxed{ \rm{ \:SI \: = \: Rs \: 4800 \: \: }}$

Hence,

$\rm \: CI \: - \: SI$

$\rm \: = \: 4992 - 4800$

$\rm \: = \: 192$

Thus,

$\rm\implies \:\boxed{ \bf{ \:CI \: - \: SI \: = \: Rs \: 192 \: \: }}$

$\rule{190pt}{2pt}$

Additional information :-

1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

$\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }}$

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

$\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: \: }}$

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

$\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }}$

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

$\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }}$

Answer 2

GIVEN :-

• P = 30000

• Time = 2 years

• Rate = 8%

TO FIND :-

• Find the difference between the compound interest and the simple interest

SOLUTION :-

A = P ( 1 + R/100)

= 30000 ( 1 + 8/100)

= 30000 (25+2/25)

= 30000 × 27/25 × 27/25

A = 34992

C.I. = A - P

34992 - 30000

= 4992

S.I. = P × R × T/100

= 30000 × 8 × 2 /100

= 4800

Difference = C.I. - S.I.

= 4992 - 4800 = 192