Question

How much would a sum of 20,000 amount to, at 12% in 9 months if the interest is being compounded quarterly.​

Answer 1

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

Given that,

Principal, P = 20000

Rate of interest, r = 12 % per annum compounded quarterly

Time = 9 months = 9/12 = 3/4 years.

We know,

Amount received on a certain sum of money of P invested at the rate of r % per annum compounded quarterly for n years is given by

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

So, on substituting the values, we get

$\rm \: \:Amount \: = \: 20000\: {\bigg[1 + \dfrac{12}{400} \bigg]}^{3} \: \:$

$\rm \: \:Amount \: = \: 20000\: {\bigg[1 + \dfrac{3}{100} \bigg]}^{3} \: \:$

$\rm \: \:Amount \: = \: 20000\: {\bigg[\dfrac{100 + 3}{100} \bigg]}^{3} \: \:$

$\rm \: \:Amount \: = \: 20000\: {\bigg[\dfrac{103}{100} \bigg]}^{3} \: \:$

$\red{\rm\implies \:\boxed{ \rm{ \:\sf \: \:Amount \: = \: 21854.54 \: \:}}}$

$\rule{190pt}{2pt}$

Additional information :-

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

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

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

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

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

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

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

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

Answer 2

QUESTION :-

• How much would a sum of 20,000 amount to, at 12% in 9 months if the interest is being compounded quarterly.

GIVEN :-

• sum of 20,000 amount to, at 12% in 9 months

TO FIND :-

• How much would a sum = ?

SOLUTION :-

• T = 9 month = 9/12 years

• A = P (1 + r/400 ) 4n

• A = 20,000 ( 1 + 12/ 4 × 100) 4 × 9/12

• A = 20,000 ( 100 + 3 / 100) 3

• = 21854.54

Hence, amount = Rs.21854.54