Question

find the compound interest on ₹ 12000 for 3/2 years at 8% per annum compound semi annually​

Answer 1

Answer:

The compound interest on ₹ 12000 for $\frac{3}{2}$ years at 8% per annum compound semi annually is ₹ 1498.37

Step-by-step explanation:

Given that,

Principal, P = Rs 12000

Rate of interest, r = 8 % per annum compounded semi annually

Time period, n = $\frac{3}{2}$ years

We know,

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

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

.So, on substituting the values, we get

$\sf \: Amount = 12000 {\left[ 1 + \dfrac{8}{200} \right]}^{3}$

$\sf \: Amount = 12000 {\left[ 1 + \dfrac{1}{25} \right]}^{3}$

$\sf \: Amount = 12000 {\left[ \dfrac{25 + 1}{25} \right]}^{3}$

$\sf \: Amount = 12000 {\left[ \dfrac{26}{25} \right]}^{3}$

$\sf \: Amount = 12000 \times \dfrac{17576}{15625}$

$\sf\implies \bf \: Amount = 13498.37$

Now,

$\sf \: Compound\:interest = Amount - Principal$

$\sf \: Compound\:interest = 13498.37 -12000$

$\sf\implies \bf \: Compound\:interest = 1498.37$

Hence, the compound interest on ₹ 12000 for $\frac{3}{2}$ years at 8% per annum compound semi annually is ₹ 1498.37

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

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

$\sf\red{A=P {(1 + \frac{r}{100}) }^{2n} }$

$\implies$$\sf{A=12,000{(1 + \frac{8}{200} )}^{3} }$

$\implies$$\sf{A=12,000 {(1 + \frac{1}{25} )}^{3} }$

$\implies$$\sf{A=12,000 {( \frac{25 + 1}{25} )}^{3} }$

$\implies$$\sf{A=12,000{( \frac{26}{25}) }^{3} }$

$\implies$$\sf{A = 12,000 × \frac{17576}{15625} }$

$\implies$$\sf{A=13498.37}$

$\sf\red{Compound \: Interest = Amount - Principal}$

$\implies$$\sf{13,498.37-12,000}$

$\implies$$\sf{1.498.37}$