Question

■QUESTION■

Find the compound interest on Rs. 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.

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Answer 1

Given:

• Principal (p) = Rs 160000
• Rate (r) = 20% = 20/4 = 5% (for quarter year)
• Time = 1year = 1 × 4 = 4 quarters

By using the formula,

● A = P (1 + R/100)n

= 160000 (1 + 5/100)4

= 160000 (105/100)4

= Rs 194481

∴ Compound Interest = A – P

= Rs 194481 – Rs 160000

= Rs 34481

$\sf{ \footnotesize{ \orange{hope \: it \: helps \: u!}}}$

Answer 2

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

Given that,

• Principal, P = Rs 160000

• Rate of interest, r = 20 % 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

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

So, on substituting the values, we get

$\rm \: CI = 160000 {\bigg[1 + \dfrac{20}{400} \bigg]}^{4 \times 1} - 160000$

$\rm \: CI = 160000 {\bigg[1 + \dfrac{1}{20} \bigg]}^{4} - 160000$

$\rm \: CI = 160000 {\bigg[\dfrac{20 + 1}{20} \bigg]}^{4} - 160000$

$\rm \: CI = 160000 {\bigg[\dfrac{21}{20} \bigg]}^{4} - 160000$

$\rm \: CI = 160000 \times \frac{194481}{160000} - 160000$

$\rm \: CI = 194481 - 160000$

$\rm\implies \:\boxed{ \bf{ \:CI \: = \: Rs \: 34481 \: }}$

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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

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

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

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