Question

If Principal = Rs 16,00 , Rate = 5 % , Time = 1 year find compound interest half yearly​

Answer 1

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

Principal, P = Rs 1600

Rate, r = 5 % per annum compounded half yearly

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 half yearly for n years is given by

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

So, on substituting the values, we get

$\rm \: CI \: = \: 1600 {\bigg[1 + \dfrac{5}{200} \bigg]}^{2} - 1600$

$\rm \: CI \: = \: 1600 {\bigg[1 + \dfrac{1}{40} \bigg]}^{2} - 1600$

$\rm \: CI \: = \: 1600 {\bigg[ \dfrac{40 + 1}{40} \bigg]}^{2} - 1600$

$\rm \: CI \: = \: 1600 {\bigg[ \dfrac{41}{40} \bigg]}^{2} - 1600$

$\rm \: CI \: = \: 1600 \times \frac{1681}{1600} - 1600$

$\rm \: CI \: = 1681 - 1600$

$\rm \: CI \: = 81$

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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 yearly for n years is given by

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

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

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

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

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

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

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

Answer 2

Answer:

Given :-

• Principal is Rs 1600, Rate of interest is 5% p.a and time is 1 year.

To Find :-

• What is the compound interest half yearly.

Formula Used :-

$\clubsuit$ Amount of Half-yearly Formula :

$\longrightarrow \sf\boxed{\bold{\pink{A =\: P\bigg\{1 + \dfrac{\frac{r}{2}}{100}\bigg\}^{2n}}}}$

$\footnotesize \longrightarrow \sf\boxed{\bold{\pink{Compound\: Interest =\: Amount - Principal}}}$

Solution :-

First, we have to find the amount :

Given :

• Principal = Rs 1600
• Rate of Interest = 5% p.a
• Time = 1 year

According to the question by using the formula we get,

$\implies \sf A =\: 1600\bigg\{1 + \dfrac{\frac{5}{2}}{100}\bigg\}^{2 \times 1}$

$\implies \sf A =\: 1600\bigg\{1 + \dfrac{5}{2} \times \dfrac{1}{100}\bigg\}^2$

$\implies \sf A =\: 1600\bigg\{1 + \dfrac{5}{200}\bigg\}^2$

$\implies \sf A =\: 1600\bigg\{\dfrac{200 + 5}{200}\bigg\}^2$

$\implies \sf A =\: 1600\bigg\{\dfrac{205}{200}\bigg\}^2$

$\implies \sf A =\: 1600 \times \dfrac{205}{200} \times \dfrac{205}{200}$

$\implies \sf A =\: \dfrac{1600 \times 205 \times 205}{200 \times 200}$

$\implies \sf A =\: \dfrac{6724\cancel{0000}}{4\cancel{0000}}$

$\implies \sf A =\: \dfrac{\cancel{6724}}{\cancel{4}}$

$\implies \sf\bold{\purple{A =\: Rs\: 1681}}$

Now, we have to find the compound interest :

Given :

• Principal = Rs 1600
• Amount = Rs 1681

According to the question by using the formula we get,

$\small \dashrightarrow \sf Compound\: Interest =\: Rs\: 1681 - Rs\: 1600$

$\small \dashrightarrow \sf\bold{\red{Compound\: Interest =\: Rs\: 81}}$

$\therefore$ The compound interest is Rs 81 .