Question

the simple interest on a sum of money for 2 years at 12 percent per annum is rupees 14400. What will be the compound interest on that sum at the same rate and for the same time?


plss say​

Answer 1

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

Case - 1 Simple Interest

Given that,

The simple interest on a sum of money for 2 years at 12 % per annum is Rs 14400.

So, we have

Time, n = 2 years

Rate of interest, r = 12 % per annum

Simple interest, SI = Rs 14400

Let assume that sum invested be Rs p.

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

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: SI \: = \: \frac{prn}{100} \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:14400 = \dfrac{p \times 12 \times 2}{100}$

$\rm :\longmapsto\:1200 = \dfrac{p \times 2}{100}$

$\rm :\longmapsto\:600 = \dfrac{p}{100}$

$\rm \implies\:\boxed{ \tt{ \: p \: = \: 60000 \: }}$

Case - 2 Compound Interest

Sum invested, p = Rs 60000

Rate of interest, r = 12 % per annum compounded annually

Time period, 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

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

So, on substituting the values, we get

$\rm :\longmapsto\:CI = 60000 {\bigg[1 + \dfrac{12}{100} \bigg]}^{2} - 60000$

$\rm :\longmapsto\:CI = 60000 {\bigg[1 + \dfrac{3}{25} \bigg]}^{2} - 60000$

$\rm :\longmapsto\:CI = 60000 {\bigg[\dfrac{25 + 3}{25} \bigg]}^{2} - 60000$

$\rm :\longmapsto\:CI = 60000 {\bigg[\dfrac{28}{25} \bigg]}^{2} - 60000$

$\rm :\longmapsto\:CI = 60000 {\bigg[\dfrac{784}{625} \bigg]} - 60000$

$\rm :\longmapsto\:CI = 60000 {\bigg[\dfrac{784}{625} - 1 \bigg]}$

$\rm :\longmapsto\:CI = 60000 {\bigg[\dfrac{784 - 625}{625}\bigg]}$

$\rm :\longmapsto\:CI = 159 \times 96$

$\rm :\longmapsto\:CI = 15264$

$\green{\rm \implies\:\boxed{ \bf{ \: CI \: = \: Rs \: 15264 \: }}}$

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Additional Information :-

1. Compound interest CI on a certain sum of money of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: CI = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} - p \: }}}$

2. Compound interest CI on a certain sum of money of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: CI = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} - p \: }}}$

3. Compound interest CI on a certain sum of money of Rs p invested at the rate of r % per annum compounded monthly for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: CI = p {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} - p \: }}}$