Question

What is the sum of money will amount to ₹18,150 in 2years at 10% per annum compounded annually

Answer 1

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

Given that

A certain sum of money will amount to ₹18,150 in 2years at 10% per annum compounded annually.

Let assume that the sum of money invested be Rs p.

So, we have

↝ Sum invested, = Rs p

↝ Time period, n = 2 years

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

↝ Amount = Rs 18, 150

We know,

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

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

On substituting the values, we get

$\rm :\longmapsto\:18150 = p {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}$

$\rm :\longmapsto\:18150 = p {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:18150 = p {\bigg[ \dfrac{10 + 1}{10} \bigg]}^{2}$

$\rm :\longmapsto\:18150 = p {\bigg[ \dfrac{11}{10} \bigg]}^{2}$

$\rm :\longmapsto\:18150 = p \times \dfrac{121}{100}$

$\rm :\longmapsto\:p = 18150 \times \dfrac{100}{121}$

$\rm \implies\:\boxed{ \tt{ \: p \: = \: Rs \: 15000 \: }}$

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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 semi - annually for n years is

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

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

$\large \red{\underline \pink{ \underline{\sf \blue{Solution}}}} \purple\downarrow$

Given that

A certain sum of money will amount to ₹18,150 in 2years at 10% per annum compounded annually.

Let assume that the sum of money invested be Rs p.

So, we have

↝ Sum invested, = Rs p

↝ Time period, n = 2 years

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

↝ Amount = Rs 18, 150

We know,

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

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

On substituting the values, we get

$\rm \blue{:\longmapsto\:18150 = p {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}}$

$\rm \orange{ :\longmapsto\:18150 = p {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}}$

$\rm \purple{:\longmapsto\:18150 = p {\bigg[ \dfrac{10 + 1}{10} \bigg]}^{2}}$

$\rm \pink{ :\longmapsto\:18150 = p {\bigg[ \dfrac{11}{10} \bigg]}^{2}}$

$\rm \red{ :\longmapsto\:18150 = p \times \dfrac{121}{100}}$

$\rm \green{ :\longmapsto\:p = 18150 \times \dfrac{100}{121}}$

$\rm \purple{ \implies\:\boxed{ \tt{ \: p \: = \: Rs \: 15000 \: }}}$

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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 semi - annually for n years is

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

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

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

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