Question

The SI on a certain sum for 3 years at 4 per cent is 600. Find the CI on the same sum
at the same rate per cent and in the same time.​

Answer 1

$\bf \: \underline{Given} :$ ↴

The Simple Interest on a certain sum for 3 years at 4 per cent is 600.

$\bf \: \underline{To \: find} :$ ↴

We have to find the Compound Interest on the same sum at the same rate % and in the same time.

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

$\sf \: First \: of \: all \: we \: have \: to \: \: find \: the \: Principal.$

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

$\sf \: \underline{Putting \: the \: values}$

$\sf \: 600 = \dfrac{P \times 4 \times 3 }{100}$

$\sf \: Rewrite \: the  \: equation  \: as$

$\sf \: \dfrac{P \times 4 \times 3 }{100} = 600$

$\sf \: Cancel \: the \:  common \: factor  \: of  \: 44 \:  and  \: 100$

$\sf \: \dfrac{P \times 3 }{25} = 600$

$\sf \: Multiply \: both \: sides \: of \: the \: equation \: by \: 25$

$\sf \: \dfrac{P \times 3 }{25} \: \times \: 25 \green{ =} 600 \: \times \: 25$

$\sf \: Simplify \: the \: expression$

$\sf \: 3P \: = \: 15000$

$\sf \: P \: = \: \dfrac{15000}{3}$

$\sf \: P \: = 5000$

$\green{ \sf \: So, \: the \: Principal \: (P) = Rs. \: 5000}$

$\sf \: Now, \: we \: will \: find \: the \: Amount..$

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

$\sf \: Here,$

$\sf \bull \longrightarrow \: Principal \: (P) = Rs. \: 5000$

$\sf \bull \longrightarrow \: Rate \: of \: interest \: (R) = 4 \: \%$

$\sf \bull \longrightarrow \: Time \: (n) = 3 \: Years$

$\sf \: \underline{Putting \: the \: values}$

$\sf \: \longrightarrow \: 5000 \bigg( 1 + \dfrac{4}{100} \bigg)^{3}$

$\sf \: Cancel \: the  \: common \: factor  \: of  \: 44 \:  and  \: 100$

$\sf \: \longrightarrow \: 5000 \bigg( 1 + \dfrac{1}{25} \bigg)^{3}$

$\sf \: Simplify \: the \: expression$

$\sf \: \longrightarrow \: 5000 \bigg( \dfrac{25 + 1}{25} \bigg)^{3}$

$\sf \:Add \:25 \: and \:1$

$\sf \: \longrightarrow \: 5000 \bigg( \dfrac{26}{25} \bigg)^{3}$

$\sf \: Simplify \: the \: expression$

$\sf \: \longrightarrow \: 5000 \bigg( \dfrac{17576}{15625} \bigg)$

$\sf \: Cancel \:the \:common \: factor \:of \:625$

$\sf \: \longrightarrow \: 8 \bigg( \dfrac{17576}{25} \bigg)$

$\sf \: Combine \: 8 \: and \: \dfrac{17576}{25}$

$\sf \: \longrightarrow \: \dfrac{8 \times 17576}{25}$

$\sf \: Multiply \:8 \: by \: 17576$

$\sf \: \longrightarrow \: \dfrac{140608}{25} \: = \: 5624.32$

$\green{ \sf \: So, \: the \: Amount \: is \: Rs. \: 5624.32}$

$\sf \: Now, \: the \: Compound \: Interest \: will \: be :$

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

$\sf \: Compound \: interest = \: 5624.32 - 5000$

$\underline{ \boxed{ \purple{\sf \: Compound \: interest = \: Rs. \: 624.32}}}$