Question

how much will a sum of 24000 amount to in 2 years at 10% per annum compounded semi annually​

Answer 1

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

Given that,

A sum of Rs 24000 invested for 2 years at 10% per annum compounded semi annually.

So, we have

↝ Sum invested, p = Rs 24000

↝ Rate of interest, r = 10 % per annum compounded semi annually.

↝ Time period, n = 2 years.

We know,

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

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

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 24000 {\bigg[1 + \dfrac{10}{200} \bigg]}^{2 \times 2}$

$\rm :\longmapsto\:Amount = 24000 {\bigg[1 + \dfrac{1}{20} \bigg]}^{4}$

$\rm :\longmapsto\:Amount = 24000 {\bigg[\dfrac{20 + 1}{20} \bigg]}^{4}$

$\rm :\longmapsto\:Amount = 24000 {\bigg[\dfrac{21}{20} \bigg]}^{4}$

$\rm \implies\:\boxed{ \tt{ \: Amount = Rs \: 29172.15 \: }}$

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Explore more :-

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

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

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

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

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

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

Answer 2

$\large \blue{\underline{\tt \green{Solution}}} \: \purple \downarrow$

Given that,

A sum of Rs 24000 invested for 2 years at 10% per annum compounded semi annually.

So, we have

↝ Sum invested, p = Rs 24000

↝ Rate of interest, r = 10 % per annum compounded semi annually.

↝ Time period, n = 2 years.

We know,

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

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

So, on substituting the values, we get

$\rm \purple{:\longmapsto\:Amount = 24000 {\bigg[1 + \dfrac{10}{200} \bigg]}^{2 \times 2}}$

$\rm \blue{ :\longmapsto\:Amount = 24000 {\bigg[1 + \dfrac{1}{20} \bigg]}^{4}}$

$\rm \green{ :\longmapsto\:Amount = 24000 {\bigg[\dfrac{20 + 1}{20} \bigg]}^{4}}$

$\rm \orange{ :\longmapsto\:Amount = 24000 {\bigg[\dfrac{21}{20} \bigg]}^{4}}$

$\rm \red{ \implies\:\boxed{ \tt{ \: Amount = Rs \: 29172.15 \: }}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬

Explore more :-

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

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

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

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

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

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