Question

The difference between the compound interest and the simple interest on a certain sum of money 16% per annum compounded annually for 2 years is Rs 600. Find sum.
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Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

The difference between the compound interest and the simple interest on a certain sum of money 16% per annum compounded annually for 2 years is Rs 600. Find sum.

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$\huge{AηsωeR} ✍$

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$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\begin{gathered}\begin{gathered}\boxed{\mathsf{ Simple\:Interest =\dfrac{Principal \times Rate \times Time}{100}}}\\\\\boxed{\mathsf{Compound\:Interest=P\bigg[ \bigg( 1+\dfrac{r}{100} \bigg)^n - 1 \bigg] }}\end{gathered}\end{gathered}$

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$\large\underline\blue{\bold{To \: Find :-  }}$

• Principal sum to be invested.

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

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$\begin{gathered}\begin{gathered}\bf Given - \begin{cases} &\sf{rate \: of \: interest, \: r \: = 16\% \: per \: annum} \\ &\sf{time, \: t = 2 \: years} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf Let - \begin{cases} &\sf{sum \: invested \: be \: Rs \: P} \end{cases}\end{gathered}\end{gathered}$

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$\large\underline\purple{\bold{❥︎ Step :- 1}}$

❥︎Calculation of Simple interest

❥︎ Principal = Rs P

❥︎ Time, t = 2 years

❥︎ Rate, r = 16% per annum

$\bf \:  ⟼ Simple \: interest , \: S_1 = \dfrac{P \times r \times t}{100}$

$\sf \:  ⟼S_1 = \dfrac{P \times 16 \times 2}{100}$

$\sf \:  ⟼S_1 = \dfrac{8P}{25} \sf \:  ⟼(1)$

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$\large\underline\purple{\bold{❥︎ Step :- 2}}$

❥︎Calculation of Compound interest

❥︎Principal = Rs P

❥︎Time, t = 2 years

❥︎Rate, r = 16% per annum

${\mathsf{Compound\:Interest \: C_1=P\bigg[ \bigg( 1+\dfrac{r}{100} \bigg)^n - 1 \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( 1+\dfrac{16}{100} \bigg)^2 - 1 \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( 1+\dfrac{4}{25} \bigg)^2 - 1 \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( \dfrac{29}{25} \bigg)^2 - 1 \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( \dfrac{841}{625} \bigg) - 1 \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( \dfrac{841 - 625}{625} \bigg) \bigg] }}$

${\mathsf{C_1=P\bigg[ \bigg( \dfrac{216}{625} \bigg) \bigg] }}\bf \:  ⟼ (2)$

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$\large\underline\purple{\bold{❥︎ Step :- 3}}$

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$\large\underline\blue{\bold{ \:According \: to \: statement :-  }}$

$\bf \:C_1 - S_1 = \: 600$

$\bf\implies \:\dfrac{216}{625} P - \dfrac{8}{25} P = 600$

$\bf\implies \:\dfrac{216P - 200P}{625} = 600$

$\bf\implies \:\dfrac{16}{625} P = 600$

$\bf\implies \:P = 600 \times \dfrac{625}{16 } = 23437.50$

$\large{\boxed{\boxed{\bf{So, sum \: invested \: is \: Rs \: 23, 437 . 50.}}}}$