Verified answer

Answer:

[tex]\boxed{\bf\:Amount = Rs \: 8741.82 \: } \\ [/tex]

Step-by-step explanation:

Given that,

Principal, P = Rs 8000

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

Time period, n = 9 months = ¾ years

We know, 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

[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }} \\ [/tex]

So, on substituting the values, we get

[tex]\sf \: Amount = 8000 {\left[ 1 + \dfrac{12}{400} \right]}^{3} \\ [/tex]

[tex]\sf \: Amount = 8000 {\left[ 1 + \dfrac{3}{100} \right]}^{3} \\ [/tex]

[tex]\sf \: Amount = 8000 {\left[ \dfrac{100 + 3}{100} \right]}^{3} \\ [/tex]

[tex]\sf \: Amount = 8000 {\left[ \dfrac{103}{100} \right]}^{3} \\ [/tex]

[tex]\sf \: Amount = 8000 \times \dfrac{1092727}{1000000} \\ [/tex]

[tex]\sf\implies \bf \: Amount = Rs \: 8741.82 \\ [/tex]

Hence,

[tex]\sf\implies \bf \: Amount = Rs \: 8741.82 \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

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

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

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

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

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

[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }} \\ [/tex]

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

[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }} \\ [/tex]