Question

ii. Determine the compound interest of Rs. 625 in 9 months at the rate of 10% per annum; interest being compounded quarterly​

Answer 1

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

Given that,

Principal, P = Rs 625

Rate of interest, r = 10 % per annum compounded quarterly

Time, n = 9 months = 3/4 years

We know,

Compound interest ( CI ) 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

$\rm \: \: \: CI \: = \: 625{\bigg[1 + \dfrac{10}{400} \bigg]}^{3} \: - \: 625 \: \:$

$\rm \: \: \: CI \: = \: 625{\bigg[1 + \dfrac{1}{40} \bigg]}^{3} \: - \: 625 \: \:$

$\rm \: \: \: CI \: = \: 625{\bigg[ \dfrac{40 + 1}{40} \bigg]}^{3} \: - \: 625 \: \:$

$\rm \: \: \: CI \: = \: 625{\bigg[ \dfrac{41}{40} \bigg]}^{3} \: - \: 625 \: \:$

$\rm \: \: \: CI \: = \: 673.06 \: - \: 625 \: \:$

$\rm\implies \:CI \: = \: 48.06$

Hence,

$\rm\implies \: \: \boxed{\sf{ \: \: \:CI \: = \: Rs \: 48.06 \: \: }}$

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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 annually 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 semi - annually for n years is given by

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

3. 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

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

4. 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

Refer the given attachment