Question

find the amount and the compound interest on rupees 20000 for one 1 by 2 years at the rate of 8% per annum compounded half yearly​

Answer 1

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

Given that,

Principal, P = Rs 20000

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

Time, n = 1 1/2 years = 3/2 years.

We know,

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

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

So, on substituting the values, we get

$\rm \: Amount = 20000 {\bigg[1 + \dfrac{8}{200} \bigg]}^{3} \:$

$\rm \: Amount = 20000 {\bigg[1 + \dfrac{1}{25} \bigg]}^{3} \:$

$\rm \: Amount = 20000 {\bigg[\dfrac{25 + 1}{25} \bigg]}^{3} \:$

$\rm \: Amount = 20000 {\bigg[\dfrac{26}{25} \bigg]}^{3} \:$

$\rm\implies \:Amount \: = \:Rs \: 22497.28$

Now, we know

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

$\rm \: = \: 22497.28 - 20000$

$\rm \: = \: 2497.28$

$\rm\implies \:Compound\:interest \: = \: Rs \: 2497.28$

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ADDITIONAL INFORMATION

1. Amount 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

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

2. Amount 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

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

3. Amount 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

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

Answer 2

Answer:

Step-by-step explanation: