Question

How much would a sum of Rs.25,000 amount to in 1-1/2years at 8%p.a. if the interest is compounded half-yearly​

Answer 1

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

Given that,

A sum of Rs.25,000 invested at the rate of 8% p.a., if the interest is compounded half-yearly for one and a half year.

So, we have

↝ Sum invested, p = Rs 25, 000

↝ Rate of interest, r = 8 % per annum compounded half yearly.

↝ Time = 3/2 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

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

So, on substituting the values, we get

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{8}{200} \bigg]}^{3} \:$

$\rm :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{1}{25} \bigg]}^{3} \:$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{25 + 1}{25} \bigg]}^{3} \:$

$\rm :\longmapsto\:Amount = 25000 {\bigg[\dfrac{26}{25} \bigg]}^{3} \:$

$\rm :\longmapsto\:Amount = 25000 \times \dfrac{26}{25} \times \dfrac{26}{25} \times \dfrac{26}{25}$

$\rm \implies\:\boxed{ \tt{ \: Amount \: = \: Rs \: 28121.60 \: }}$

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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

$\large\underline{\tt{\pink{Solution-}}}$

Given that,

A sum of Rs.25,000 invested at the rate of 8% p.a., if the interest is compounded half-yearly for one and a half year.

So, we have

↝ Sum invested, p = Rs 25, 000

↝ Rate of interest, r = 8 % per annum compounded half yearly.

↝ Time = 3/2 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

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

So, on substituting the values, we get

$\rm\pink{:\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{8}{200} \bigg]}^{3}} \:$

$\rm\green{ :\longmapsto\:Amount = 25000 {\bigg[1 + \dfrac{1}{25} \bigg]}^{3}} \:$

$\rm\purple{ :\longmapsto\:Amount = 25000 {\bigg[\dfrac{25 + 1}{25} \bigg]}^{3}} \:$

$\rm\blue{ :\longmapsto\:Amount = 25000 {\bigg[\dfrac{26}{25} \bigg]}^{3}}\:$

$\rm\orange{ :\longmapsto\:Amount = 25000 \times \dfrac{26}{25} \times \dfrac{26}{25} \times \dfrac{26}{25}}$

$\rm\blue{ \implies\:\boxed{ \tt{ \: Amount \: = \: Rs \: 28121.60 \: }}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬

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

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

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

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

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

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