Question

Find the amount and the compound interest on rs 20000 for 3/2 years at 10percent per annum compounded half-yearly

Answer 1

A=20000(1+10/200)^3

=20000(1+1/20)^3 =20000(21/20)(21/20)(21/20)

=(441×105)/2

=46305/2

=23152.5

CI=23152.5-20000=3152.5

Answer 2

Answer:

$\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:Amount = Rs \: 23152.50 \qquad \: \\ \\& \qquad \:\sf \:Compound\:interest = Rs \: 3152.50 \end{aligned}} \qquad \:$

Step-by-step explanation:

Given that,

Principal, P = Rs 20000

Rate of interest, r = 10 % per annum compounded half yearly

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

We know,

Amount received 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

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

.So, on substituting the values, we get

$\sf \: Amount = 20000 {\left[ 1 + \dfrac{10}{200} \right]}^{3}$

$\sf \: Amount = 20000 {\left[ 1 + \dfrac{1}{20} \right]}^{3}$

$\sf \: Amount = 20000 {\left[ \dfrac{20 + 1}{20} \right]}^{3}$

$\sf \: Amount = 20000 {\left[ \dfrac{21}{20} \right]}^{3}$

$\sf \: Amount = 20000 \times \dfrac{9261}{8000}$

$\sf\implies \bf \: Amount = Rs \: 23152.50$

Now,

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

$\sf \: Compound\:interest = 23152.50 -20000$

$\sf\implies \bf \: Compound\:interest = Rs \: 3152.50$

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

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

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