Question

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Answer 1

Answer:

Rs. 12

Step-by-step explanation:

Simple Interest:

P=Rs 4800 r=5%p.a t=2 years

∴SI=

100

Ptr

=Rs.

100

4800×2×5

=Rs 480

Compound interest:

Case I

P=Rs 4800 r=5%p.a. t=1 year

Interest =Rs.

100

4800×5×1

=Rs 240

∴A=Rs (4800+240)=Rs 5040

Case II

P=Rs 5040 r=5%p.a. t=1 year

Interest =Rs.

100

5040×5×1

=Rs 252.

∴A=Rs (5040+252)=Rs 5292.

∴ Compound Interest =Rs(5292−4800)=Rs 492

∴ Difference between compound Interest and Simple Interest =Rs (492−480)=Rs.12

HOPE IT HELPS

Answer 2

Answer:

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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Learn More :

$\dashrightarrow{\small{\underline{\boxed{\sf{\purple{Simple \: Interest = \dfrac{P \times R \times T}{100}}}}}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\purple{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\purple{Amount = Principle + Interest}}}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\purple{ Principle=Amount - Interest }}}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\purple{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}}$

$\dashrightarrow\small{\underline{\boxed{\sf{\purple{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}}}$

${\underline{\rule{220pt}{2.5pt}}}$