Question

Find the Amount and the Compound Interest on Rs 125000 for 1 1/2 years at 4% per annum compounded half-yearly.​

Answer 1

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

Given that,

Principal, P = Rs 125000

Rate of interest, r = 4 % per annum compounded half yearly.

Time, n = 1 1/2 years = 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 given by

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

On substituting the values, we get

$\rm \: Amount \: = \: 125000 {\bigg[1 + \dfrac{4}{200} \bigg]}^{3}$

$\rm \: Amount \: = \: 125000 {\bigg[1 + \dfrac{2}{100} \bigg]}^{3}$

$\rm \: Amount \: = \: 125000 {\bigg[ \dfrac{100 + 2}{100} \bigg]}^{3}$

$\rm \: Amount \: = \: 125000 {\bigg[ \dfrac{102}{100} \bigg]}^{3}$

$\rm \: Amount \: = \: 125000 {\bigg[ 1.02 \bigg]}^{3}$

$\rm\implies \:Amount \: = \: 132651$

We know,

$\rm \: Compound\:Interest \: = \: Amount \: - \: P \:$

$\rm \: = \: 132651 - 125000$

$\rm \: = \: 7651$

So,

$\rm\implies \:Compound\:Interest \: = \: 7651$

Hence,

Amount = Rs 132651

and

Compound Interest = Rs 7651

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Additional Information :-

1. Amount 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

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

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 given by

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

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 given by

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

Answer 2

Step-by-step explanation:

$\color{blue} \text{Given, \( \tt P=125000 \: R S, t=1 \dfrac{1}{2}=\dfrac{3}{2} \) years, Rate\( \tt R=4 \% \)}$

Find Amount and compound interest :

$\color{red} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline\hline\hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

$\color{indigo} \text{ \( \tt R=4 \% \: \: \Rightarrow R=\dfrac{4}{2}=2 \% \) for half yeariy}$

$\color{olive} \[ \begin{array}{l} \tt A=P\left(1+\dfrac{R}{100}\right)^{n} \qquad(\therefore n= \text{time } =3 \: \: \text{half \: yearly)} \\ \\ \tt A=125000\left(1+\dfrac{2}{100}\right)^{3} \\ \\ \tt A=125000\left(\dfrac{106}{100}\right)^{3} \\ \\ \tt A=125000\left(\dfrac{53}{50}\right)^{3} \\ \\ \tt A=125000 \times \dfrac{53}{50} \times \dfrac{53}{50} \times \dfrac{53}{50} \\ \\ \tt A=148877 Rs \\ \\ \tt\text {( Compound Interest) } C I=A-P \\ \\ \tt C I=148877-125000 \\ \\ \tt \boxed{ \tt \: C I =23877 \text { Rs. }} \end{array} \]$

Hence, Amount =148877 Rs and C I=23877 Rs.