Question

Find the compound interest (payable yearly) and amount on 240 for 2 years at 4% per annum.​ PLS SEND THE PICTURE OF ANSWER

Answer 1

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

Principal, p = Rs 240

Rate of interest, r = 4 % per annum compounded annually

Time, n = 2 years

We know,

Amount (A) on a certain sum of money of Rs p invested at the rate of r % per annum compounded annually for n years is

$\red{\boxed{\tt{ \: \: Amount \: = \: p \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }}}$

So, on substituting the values of p, r and n, we get

$\rm \: Amount = 240 {\bigg[1 + \dfrac{4}{100} \bigg]}^{2}$

$\rm \: Amount = 240 {\bigg[1 + \dfrac{1}{25} \bigg]}^{2}$

$\rm \: Amount = 240 {\bigg[ \dfrac{25 + 1}{25} \bigg]}^{2}$

$\rm \: Amount = 240 {\bigg[ \dfrac{26}{25} \bigg]}^{2}$

$\rm \: Amount = 240 \times \dfrac{26}{25} \times \dfrac{26}{25}$

$\rm\implies \:Amount = Rs \: 259.58 \: \: \: \: (approx)$

Now, We know

Compound Interest on a certain sum of money of Rs p, amounts to Rs A at r % per annum compounded annually for n years is given by

$\red{\boxed{\tt{ \: \: Compound \: Interest \: = \: Amount \: - \: p \: }}}$

So, on substituting the values, we get

$\rm \: Compound \: Interest \: = \: 259.58 - 240$

$\rm\implies \:Compound \: Interest \: = \: Rs \: 19.58$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

ADDITIONAL INFORMATION

1. Amount (A) on a certain sum of money of Rs p invested at the rate of r % per annum compounded semi - annually for n years is

$\red{\boxed{\tt{ \: \: Amount \: = \: p \: {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: \: }}}$

2. Amount (A) on a certain sum of money of Rs p invested at the rate of r % per annum compounded quarterly for n years is

$\red{\boxed{\tt{ \: \: Amount \: = \: p \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }}}$

3. Amount (A) on a certain sum of money of Rs p invested at the rate of r % per annum compounded monthly for n years is

$\red{\boxed{\tt{ \: \: Amount \: = \: p \: {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }}}$

Answer 2

Step-by-step explanation:

$\sf \large \red{Given:-}$

$\tt Principal = 240 \: \: rs.$

$\tt time = 2 \: years$

$\tt rate = 4 \rm{ \%} \: p.a.$

$\sf \large \red{Solution:-}$

$\boxed{\rm Amount= p \bigg( 1+ \dfrac{R}{100} \bigg)^n}$

$\tt : \implies 240 \bigg( 1+ \dfrac{4}{100} \bigg) ^2$

$\tt : \implies 240 \bigg( \dfrac{104}{100} \bigg) ^2$

$\tt : \implies 240 \bigg( \dfrac{26}{25} \bigg) ^2$

$\tt : \implies 240 \bigg( \dfrac{676}{625} \bigg)$

$\tt : \implies 259.584 \: \: rs.$

$\boxed{\rm C.I = A-P}$

$\tt : \implies 259.584-240$

$\tt : \implies 19.584 \: \: rs.$