Question

Kala borrowed ` 25000 from her friend at 12% per annum simple interest. She lent it to
Subha at the same rate but compounded annually. How much is her gain after 2 years?

Answer 1

$\bf \: \underline{Given }\: :$ ↴

$\sf \: Present \: value \: : \: Rs. 25000$

$\sf \: Interest \: rate \: : \: 12 \% \: per \: annum$

$\sf \: Time \: : \: 2 \: Years$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: Amount \: for \: Money \: after \: 2 \: years.$

$\sf \: \underline{Formula \: to \: be \: used} :$ ↴

$\boxed{ \pink{ \sf \: Simple \: Interest \: (SI) \: = \: \dfrac{P \times R \times T }{100} }}$

$\boxed{ \pink{\sf \: Amount \: (A) \: = \: P \bigg(1+ \: \dfrac{R }{100} \bigg) ^{n} }}$

$\star \: \bf \: \underline{So, \: Let's \: Start} \: \star$

$\sf \: First \: of \: all \: we \: will \: find \: Simple \: Interest.$

$\sf \: Simple \: Interest : \dfrac{25000\times 12 \times 2 }{100}$

$\sf \: Simple \: Interest : \dfrac{250\times 12 \times 2 }{1}$

$\sf \therefore \: 250\times 12 \times 2 \: = \: Rs. \: 6000$

$\sf \purple{So, \: Simple \: \: Interest \: = \: Rs. \: 6000 }$

$\sf \: Now, \: Amount \: will \: be \: :$

$\sf \: Amount \: (A) \: = \: P \bigg(1+ \: \dfrac{R }{100} \bigg) ^{n}$

$\sf \: Putting \: the \: values..$

$\sf \: Amount \: (A) \: = \: 25000 \bigg(1+ \: \dfrac{12}{100} \bigg) ^{2}$

$\sf \: Amount \: (A) \: = \: 25000 \bigg(\dfrac{112}{100} \bigg) ^{2}$

$\sf \: Amount \: (A) \: = \: 25000 \times \bigg(\dfrac{112}{100} \: \times \: \dfrac{112}{100} \bigg)$

$\sf \: Amount \: (A) \: = \: 25000 \times \dfrac{12544}{10000}$

$\sf \: Amount \: (A) \: = \: 25 \times \dfrac{12544}{10}$

$\sf \: Amount \: (A) \: = \: 5 \times \dfrac{6272}{1}$

$\sf \therefore 5 \times 6272 \: = \:Rs. \: 31360$

$\sf \purple{So, \: Amount \: = \: Rs. \: 31360 }$

$\sf \: Now, \: we \: will \: find \: \: the \: Compound \: Interest.$

$\pink{ \boxed { \sf \: Compound \: I nterest = Amount - Principal}}$

$\sf \: Compound \: Interest = 31360 - 25000$

$\sf \: Compound \: Interest = Rs. \: 6360$

$\bf \: Now,$

$\sf \: Compound \: interest \: - \: Simple \: Interest$

$\sf \longrightarrow \: \: 6360 \: - \: 6000$

$\sf \longrightarrow Rs. \: 360$

$\green{ \sf \:\underline{ Hence \: our \: answer \: is \: \red{ \sf \: Rs. \: 360 }}}$

Answer 2

Given :

• Principal (P) = 25000
• Rate of interest (r) = 12%
• Time (n) = 2 years

$\:$

To find :

• How much is her gain after 2 years.

$\:$

Solution :

• In the question Principal, rate of intrerst and time is given. Firstly we will find the simple interest and then amount and then Compound Interest. Compound interest will be the money she will gain after 2 years.

$\:$

${ \underline{ \boxed{ \red{ \sf{S.I = \frac{P × R × T}{100} }}}}}$

$\:$

$~~~~~$➤ 25000 × 12 × 2

$~~~~~$➤ 250 × 12 × 2

$~~~~~$➤ 6000

$\:$

${ \underline{ \boxed{ \red{ \sf{Amount = P \bigg( { 1 + \dfrac{r}{100} \bigg)}^{n} }}}}}$

$\:$

$~~~~~$➤ 25000 (1 + 12/100)²

$~~~~~$➤ 25000 × 112/100 × 112/100

$~~~~~$➤ 25 × 112 × 112

$~~~~~$➤ 31360

$\:$

${ \underline{ \boxed{ \red{ \sf{C.I = Amount - Principal }}}}}$

$~~~~~$➤ 31360 - 25000

$~~~~~$➤ 6360

$\:$

She will gain after 2 years.

$~~~~~$➤ 6300 - 6000

$~~~~~$➤ 360

$\:$

${ \underline{ \boxed{ \pink{ \bf{She \: will \: Gain \: Rs. 360~after~2~years}}}}}$

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