Question

Pooja deposited Rs. 6000 in a bank which pays interest at the rate of 10% p.a. compounded
quarterly, find the interest due to Pooja after 1 year?​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given -   \begin{cases} &\sf{Principal \: = \: Rs. \: 6000} \\ &\sf{ Rate \: = 10 \: \% \: per \: annum}\\ &\sf{Time \: = \: 1 \: year} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find  - \begin{cases} &\sf{Interest \: after \: 1 \: year}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Here,

Given that

• Principal, P = Rs 6000

• Rate of Interest, R = 10 % per annum

• Time, n = 1 year

~ Using formula of Amount when interest is compounded quarterly,

${\sf{\star \boxed{ \green{ \rm \: Amount \: = \: P(1+ \dfrac{R}{400})^{4n}}}}}$

where,

• P denotes Principal

• R denotes Rate per annum

• n denotes time in years

$\rm : \implies \:Amount \: = \: 6000 { \bigg(1 + \dfrac{10}{400} \bigg) }^{4 \times 1}$

$\rm : \implies \:Amount \: = \: 6000 { \bigg(1 + \dfrac{1}{40} \bigg) }^{4 }$

$\rm : \implies \:Amount \: = \: 6000 { \bigg(\dfrac{40 + 1}{40} \bigg) }^{4 }$

$\rm : \implies \:Amount \: = \: 6000 { \bigg(\dfrac{41}{40} \bigg) }^{4 }$

$\boxed{ \purple{ \rm : \implies \:Amount \: = \: Rs. \: 6622. \: 88}}$

Now, Compound interest is evaluated by

${\sf{\star \: \boxed{ \pink{ \rm \: CI \: = Amount \: - Principal}}}}$

$\rm : \implies \:CI \: = \: 6622.88 \: - \: 6000$

$\boxed{ \pink{ \rm : \implies \:CI \: = \: Rs. \: 622. \: 88}}$