Question

find the compound interest on a sum of RS 12000 at the rate of 8% per annum for 1 year compounded quarterly. please step by step ​

Answer 1

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

Principal, P = Rs 12000

Rate of interest, r = 8 % per annum compounded quarterly.

Time, n = 1 year

We know,

Compound interest (CI) 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

$\boxed{\sf{ \: \: CI \: = \: P {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} - P \: \: }}$

So, on substituting the values, we get

$\rm \: \: CI \: = \: 12000 {\bigg[1 + \dfrac{8}{400} \bigg]}^{4} - 12000 \: \:$

$\rm \: \: CI \: = \: 12000 {\bigg[1 + \dfrac{1}{50} \bigg]}^{4} - 12000 \: \:$

$\rm \: \: CI \: = \: 12000 {\bigg[ \dfrac{50 + 1}{50} \bigg]}^{4} - 12000 \: \:$

$\rm \: \: CI \: = \: 12000 {\bigg[ \dfrac{51}{50} \bigg]}^{4} - 12000 \: \:$

$\rm \: CI = 12989.18 - 12000$

$\rm\implies \:CI = 989.18$

So,

Compound interest received on Rs 12000 at the rate of 8% per annum compounded quarterly for 1 year is Rs 989.18

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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

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

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

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

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

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

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

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

Answer 2

Answer:

Given :-

• A sum of Rs 12000 at the rate of 8% per annum for 1 year compounded quarterly.

To Find :-

• What is the compound interest.

Formula Used :-

$\clubsuit$ Amount Formula when the interest is compounded quarterly :

$\dashrightarrow \sf\boxed{\bold{\pink{A =\: P\Bigg(1 + \dfrac{\dfrac{r}{4}}{100}\Bigg)^{4n}}}}$

$\bigstar$ Compound Interest Formula :

$\dashrightarrow \sf\boxed{\bold{\pink{Compound\: Interest =\: A - P}}}$

Solution :-

First, we have to find the amount :

Given :

• Principal = Rs 12000
• Rate of Interest = 8% per annum
• Time Period = 1 year

According to the question by using the formula we get,

$\implies \sf A =\: 12000\Bigg(1 + \dfrac{\dfrac{\cancel{8}}{\cancel{4}}}{100}\Bigg)^{(4 \times 1)}$

$\implies \sf A =\: 12000\bigg(1 + \dfrac{2}{100}\bigg)^4$

$\implies \sf A =\: 12000\bigg(\dfrac{100 + 2}{100}\bigg)^4$

$\implies \sf A =\: 12000\bigg(\dfrac{\cancel{102}}{\cancel{100}}\bigg)^4$

$\implies \sf A =\: 12000\bigg(\dfrac{51}{50}\bigg)^4$

$\implies \sf A =\: 12000 \times \dfrac{51}{50} \times \dfrac{51}{50} \times \dfrac{51}{50} \times \dfrac{51}{50}$

$\implies \sf A =\: 12{\cancel{000}} \times \dfrac{6765201}{6250\cancel{000}}$

$\implies \sf A =\: 12 \times \dfrac{6765201}{6250}$

$\implies \sf A =\: \dfrac{12 \times 6765201}{6250}$

$\implies \sf A =\: \dfrac{81182412}{6250}$

$\implies \sf\bold{\purple{A =\: Rs\: 12989.18}}$

Now, we have to find the compound interest :

Given :

• Amount = Rs 12989.18
• Principal = Rs 12000

According to the question by using the formula we get,

$\longrightarrow \sf Compound\: Interest =\: Rs\: 12989.18 - Rs\: 12000$

$\longrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 989.18}}$

$\therefore$ The compound interest is Rs 989.18 .