Question

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Answer 1

Given Question :-

Arjun deposited Rs 25000 in a bank at the rate of 6 % per annum compounded half yearly. What amount he will receive at the end of 1 1/2 years ?

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

Given that,

Arjun deposited Rs 25000 in a bank at the rate of 6 % per annum compounded half yearly for one and a half year.

So, we have

Principal, p = Rs 25000

Rate, r = 6 % per annum compounded half yearly

Time, n = 1.5 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

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

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{6}{200} \bigg]}^{2 \times 1.5}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{3}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{100 + 3}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{103}{100} \bigg]}^{3}$

$\rm :\longmapsto\:Amount = 25000 \times {\bigg[\dfrac{103}{100} \bigg]} \times \bigg[\dfrac{103}{100} \bigg] \times \bigg[\dfrac{103}{100} \bigg]$

$\rm :\longmapsto\:Amount = 27318.17 \: (approx.)$

Hence,

• Arjun will receive Rs 27318. 17.

Additional Information :

1. Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded yearly for n years is

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

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

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

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

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

4. Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded yearly for n years, y % per annum compounded annually for m years is

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