Question

The difference between compound interest and simple interest at 5% per annum in 2 years is 30. Find the sum.​

Answer 1

Given :

• The difference between compound interest and simple interest at 5% per annum in 2 years is 30.

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To find :

• Sum?

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Solution :

Difference between CI & SI for 2 years :

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$\star\;{\boxed{\sf{\purple{ \dfrac{S.I. = P \times R \times T}{100}}}}}$

Putting values,

$:\implies\sf S.I ={\dfrac{Principal \times Rate \times Time}{100}}$

$:\implies\sf S.I.=\dfrac{Principal \times {\cancel {5}} \times 2}{100}$

$:\implies\sf S.I. =\dfrac{Principal}{10}$

And,

$:\implies\sf Amount = P {\dfrac{1+5}{100}^2}$

$:\implies\sf Amount =P {\dfrac{21}{20}^2}$

$:\implies\sf Amount =P {\dfrac{441}{400}^2}$

$:\implies\sf C.I. = Amount - Principal$

$:\implies\sf C.I. = \dfrac{441 P}{400} - Principal$

$:\implies\sf C.I. = \dfrac{441 P - 400 P}{400}$

$:\implies\sf C.I. = \dfrac{41 P}{400}$

$:\implies\sf C.I. - S.I. = Rs. 30$

$:\implies\sf \dfrac{41 P}{400} - \dfrac{P}{100} = 30$

$:\implies{\boxed{\sf{\pink{Principal = Rs. \:12000 }}}}\;\bigstar$

$\therefore\:\underline{\textsf{Hence, the sum is \textbf{Rs. 12,000}}}.$

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Answer 2

Given :

The difference between compound interest and simple interest at 5% per annum in 2 years is 30.

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To find :

Sum?

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Solution :

Difference between CI & SI for 2 years :

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\purple{ \dfrac{S.I. = P \times R \times T}{100}}}}}$

Putting values,

$:\implies\sf S.I ={\dfrac{Principal \times Rate \times Time}{100}}$

$:\implies\sf S.I.=\dfrac{Principal \times {\cancel {5}} \times 2}{100}$

$:\implies\sf S.I. =\dfrac{Principal}{10}$

And,

$:\implies\sf Amount = P {\dfrac{1+5}{100}^2}$

$:\implies\sf Amount =P {\dfrac{21}{20}^2}$

$:\implies\sf Amount =P {\dfrac{441}{400}^2}$

$:\implies\sf C.I. = Amount - Principal$

$:\implies\sf C.I. = \dfrac{441 P}{400} - Principal$

$:\implies\sf C.I. = \dfrac{441 P - 400 P}{400}$

$:\implies\sf C.I. = \dfrac{41 P}{400}$

$:\implies\sf C.I. - S.I. = Rs. 30$

$:\implies\sf \dfrac{41 P}{400} - \dfrac{P}{100} = 30$

$:\implies{\boxed{\sf{\pink{Principal = Rs. \:12000 }}}}\;\bigstar$

$\therefore\:\underline{\textsf{Hence, the sum is \textbf{Rs. 12,000}}}.$

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