Question

Find the amount of Rs 1000 in one year at 2% per annum, when the interest is compounded half-yearly.​

Answer 1

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

Given that,

• Principal, P = Rs 1000

• Rate of interest, r = 2 % per annum compounded half yearly.

• Time, n = 1 year.

We know,

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

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

So, on substituting the values, we get

$\rm \: Amount = 1000 {\bigg[1 + \dfrac{2}{200} \bigg]}^{2 \times 1}$

$\rm \: Amount = 1000 {\bigg[1 + \dfrac{1}{100} \bigg]}^{2}$

$\rm \: Amount = 1000 {\bigg[\dfrac{100 + 1}{100} \bigg]}^{2}$

$\rm \: Amount = 1000 {\bigg[\dfrac{101}{100} \bigg]}^{2}$

$\rm \: Amount = 1000 \times \dfrac{101}{100} \times \dfrac{101}{100}$

$\rm \: Amount = \dfrac{10201}{10}$

$\red{\rm\implies \:\boxed{ \rm{ \:Amount \: = \: Rs \: 1020.10 \: }}}$

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

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:

the answer is Amount=Rs1020.10 , You can verify if by methods