Question

The difference between SI and CI on a certain sum is ₹54.40 for 2 years at 8% p.a. Find the sum.​

Answer 1

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

Let us assume that sum be Rs x.

Case :- 1 Compound interest

Principal, P = Rs x

Time, n = 2 years

Rate, r = 8 % per annum compounded annually.

We know,

Compound interest on a certain sum of money Rs P invested at the rate of r % per annum compounded annually for n years is

$\bf :\longmapsto\: CI=P\bigg(1+\dfrac{r}{100}\bigg)^{n}-P$

On substituting the values, we get

$\tt{\implies CI=x\bigg(1+\dfrac{8}{100}\bigg)^{2}-x}$

$\tt{\implies CI=x\bigg(1+\dfrac{2}{25}\bigg)^{2}-x}$

$\tt{\implies CI=x\bigg(\dfrac{25 + 2}{25}\bigg)^{2}-x}$

$\tt{\implies CI=x\bigg(\dfrac{27}{25}\bigg)^{2}-x}$

$\tt{\implies CI=x\bigg(\dfrac{729}{625}\bigg)-x}$

$\tt{\implies CI=\dfrac{729x - 625x}{625}}$

$\bf{\implies CI=\dfrac{104x}{625}} - - - (1)$

Case :- 2 Simple Interest

Principal, P = Rs x

Time, n = 2 years

Rate, r = 8 % per annum.

We know,

Simple interest on a certain sum of money Rs p invested at the rate of r % per annum compounded annually for n years is

$\rm :\longmapsto\:Simple Interest, \: SI = \dfrac{p \times r \times t}{100}$

On substituting the values, we get

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

$\rm :\longmapsto\:SI = \dfrac{4x}{25} - - - (2)$

According to statement,

$\rm :\longmapsto\:CI - SI = 54.40$

On substituting the values from equation (1) and (2), we get

$\rm :\longmapsto\:\dfrac{104x}{625} - \dfrac{4x}{25} = 54.40$

$\rm :\longmapsto\:\dfrac{104x - 100x}{625} = 54.40$

$\rm :\longmapsto\:\dfrac{4x}{625} = 54.40$

$\bf\implies \:x = 8500$

Hence,

• Sum is Rs 8500

Additional Information :-

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

$\tt{\implies Amount=P\bigg(1+\dfrac{r}{100}\bigg)^{n}}$

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

$\tt{\implies Amount=P\bigg(1+\dfrac{r}{200}\bigg)^{2n}}$

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

$\tt{\implies Amount=P\bigg(1+\dfrac{r}{400}\bigg)^{4n}}$