Question

Find the difference between the simple interest and compound interest on Rs. 4800 for 2 years at 5% per annum compound interest being reckoned annually

Answer 1

Question :

Find the difference between the simple interest and compound interest on Rs.4800 for 2 years at 5% per annum, compound interest being reckoned annually.

$\begin{gathered}\end{gathered}$

Given :

Principle = Rs.4800

Time period = 2 years

Rate of Interest = 5% per annum

$\begin{gathered}\end{gathered}$

To Find :

Simple Interest

Amount

Compound Interest

Difference between the simple interest and compound interest

$\begin{gathered}\end{gathered}$

Using Formulas :

$\longrightarrow\small{\underline{\boxed{\bf{ S.I = \dfrac{P \times R \times T}{100}}}}}$

$\longrightarrow\small{\underline{\boxed{\bf{A= P\bigg(1 + \dfrac{ {R}}{100} \bigg)^{T}}}}}$

$\longrightarrow\small{\underline{\boxed{\bf{{C.I=A- P}}}}}$

$\longrightarrow\small{\underline{\boxed{\bf{Difference = C.I - S.I}}}}$

⚘ Where :-

➛ S.I = Simple Interest

➛ A = Amount

➛ P = Principle

➛ R = Rate

➛ T = Time

➛ C.I = Compound Interest

$\begin{gathered}\end{gathered}$

Solution :

⚘ Finding the simple interest by substituting the values in the formula :-

$\dashrightarrow\small{\sf{ S.I = \dfrac{P \times R \times T}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{4800 \times 5 \times 2}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{4800 \times 10}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{48000}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \cancel{\dfrac{48000}{100}}}}$

$\dashrightarrow\small{\sf{S.I = Rs.480}}$

$\longrightarrow\small{\underline{\boxed{\sf{\pink{S.I = Rs.480}}}}}$

∴ The simple interest is Rs.480.

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⚘ Finding amount by substituting the values in the formula :-

$\dashrightarrow\small{\sf{A= P\bigg(1 + \dfrac{ {R}}{100} \bigg)^{T}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg(1 + \dfrac{{5}}{100} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg(\dfrac{(1 \times 100) + (5 \times 1)}{100} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg(\dfrac{100+5}{100} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg(\dfrac{105}{100} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg( \cancel{\dfrac{105}{100}} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg( {\dfrac{21}{20}} \bigg)^{2}}}$

$\dashrightarrow\small{\sf{A= 4800\bigg( {\dfrac{21}{20}} \times \dfrac{21}{20} \bigg)}}$

$\dashrightarrow\small{\sf{A= 4800\bigg( {\dfrac{21 \times 21}{20 \times 20}} \bigg)}}$

$\dashrightarrow\small{\sf{A= 4800\bigg( {\dfrac{441}{400}} \bigg)}}$

$\dashrightarrow\small{\sf{A= 4800 \times {\dfrac{441}{400}}}}$

$\dashrightarrow\small{\sf{A= \cancel{4800} \times {\dfrac{441}{\cancel{400}}}}}$

$\dashrightarrow\small{\sf{A=12 \times 441}}$

$\dashrightarrow\small{\sf{A=Rs.5292}}$

$\longrightarrow\small{\underline{\boxed{\sf{\pink{Amount=Rs.5292}}}}}$

∴ The amount is Rs.5292.

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⚘ Finding compound interest by substituting the values in the formula :-

$\dashrightarrow{\small{\sf{{C.I=A- P}}}}$

$\dashrightarrow{\small{\sf{{C.I=5292- 4800}}}}$

$\dashrightarrow{\small{\sf{{C.I=492}}}}$

$\longrightarrow{\small{\underline{\boxed{\sf{\pink{{C.I=492}}}}}}}$

∴ The compound interest is Rs.492.

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⚘ Now, finding the difference between Compound interest and Simple interest :-

$\dashrightarrow\small{\sf{Difference = C.I - S.I}}$

$\dashrightarrow\small{\sf{Difference = 492- 480}}$

$\dashrightarrow\small{\sf{Difference = Rs.12}}$

$\longrightarrow\small{\underline{\boxed{\sf{\pink{Difference = Rs.12}}}}}$

∴ The difference between simple interest and compound interest is Rs.12.

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