Question

if Principal amount is 4,00,000 Rs, rate =20% and Time =2 years. find the compound interest and amount. ​

Answer 1

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

Principal, P = Rs 400000

Rate of interest, r = 20 % per annum compounded annually.

Time, n = 2 years

We know,

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

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

So, on substituting the values, we get

$\rm \: Amount = 400000 {\bigg[1 + \dfrac{20}{100} \bigg]}^{2}$

$\rm \: Amount = 400000 {\bigg[1 + \dfrac{1}{5} \bigg]}^{2}$

$\rm \: Amount = 400000 {\bigg[ \dfrac{5 + 1}{5} \bigg]}^{2}$

$\rm \: Amount = 400000 {\bigg[ \dfrac{6}{5} \bigg]}^{2}$

$\rm \: Amount = 400000 \times \frac{36}{25}$

$\rm \: Amount = 16000 \times 36$

$\rm\implies \:\boxed{ \rm{ \:Amount \: = \: Rs \: 5, \: 76, \: 000 \: }}$

Now,

$\rm \: Compound\:interest = Amount - P$

$\rm \: Compound\:interest = 576000 - 400000$

$\rm\implies\boxed{ \rm{ \:Compound\:interest \: = \: Rs \: 1, \: 76, \: 000 \: \: }}$

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

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

Answer:

Step-by-step explanation:

Given:

Principle = p = 4,00,000

Rate of interest = 20%

Time = 2 yrs

Have to find:

Compound interest and Amount

Formula used

$CI = P[(1+i)^n-1]$

$Amt = p(1+i)^n$

Solution:

$CI = P[(1+i)^n-1]$

$CI = 4,00,000[(1+0.2)^2-1]$

$CI = 4,00,000[(1.2)^2-1]$

$[(1.2)^2-1] = 0.44$

$CI = 4,00,000 * 0.44$

$CI = 1,76,000$

Hence the compound interest of 4,00,000 for 2 yrs @ 20% is 1,76,000

Amount = Principle + Compound interest

Amount = 4,00,000 + 1,76,000

Amount = 5,76,000

                Another method to find Amount

$Amt = p(1+i)^n$

$Amt = 4,00,000(1+0.2)^2$

$Amt = 4,00,000(1.2)^2$

$(1.2)^2 = 1.44$

$Amt = 4,00,000 * 1.44$

$Amt = 5,76,000$