Question

The difference between Compound interest and Simple interest on Rs 50,000 at 5% p.a for one year is …………………… *
500
5000
0
100

Answer 1

Answer:

Gɪᴠᴇɴ :

• ➛ Principle = Rs.50000
• ➛ Rate = 5% per annum
• ➛ Time = 1 year

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

Tᴏ Fɪɴᴅ :

• ➛ Simple Interest
• ➛ Compound Interest
• ➛ Difference between Compound interest and Simple interest

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

Usɪɴɢ Fᴏʀᴍᴜʟᴀs :

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

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

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

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

☼ Where :-

• ➛ S.I = Simple Interest
• ➛ A = Amount
• ➛ P = Principle
• ➛ R = Rate
• ➛ T = Time
• ➛ C.I = Compound Interest

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

Sᴏʟᴜᴛɪᴏɴ :

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

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

$\dashrightarrow\small{\sf{ S.I = \dfrac{50000 \times 5 \times 1}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{50000 \times 5}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{250000}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \cancel{\dfrac{250000}{100}}}}$

$\dashrightarrow\small{\sf{ S.I = {Rs.2500}}}$

$\longrightarrow\small{\underline{\boxed{\sf{ Simple \: Interest = {Rs.2500}}}}}$

∴ The simple interest is Rs.2500.

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

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

$\dashrightarrow\small{\sf{A= 50000\bigg(1 + \dfrac{5}{100} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg(\dfrac{(1 \times 100) + (5 \times 1)}{100} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg(\dfrac{100+5}{100} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg(\dfrac{105}{100} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg( \cancel{\dfrac{105}{100}} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg( {\dfrac{21}{20}} \bigg)^{1}}}$

$\dashrightarrow\small{\sf{A= 50000\bigg( {\dfrac{21}{20}} \bigg)}}$

$\dashrightarrow\small{\sf{A= 50000 \times {\dfrac{21}{20}}}}$

$\dashrightarrow\small{\sf{A= \cancel{50000} \times {\dfrac{21}{\cancel{20}}}}}$

$\dashrightarrow\small{\sf{A= 2500 \times 21}}$

$\dashrightarrow\small{\sf{A= Rs.52500}}$

$\longrightarrow\small{\underline{\boxed{\sf{Amount= Rs.52500}}}}$

∴ The amount is Rs.52500.

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

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

$\dashrightarrow{\small{\sf{{C.I=52500- 50000}}}}$

$\dashrightarrow{\small{\sf{{C.I=Rs.2500}}}}$

$\longrightarrow{\small{\underline{\boxed{\sf{{Compound \: Interest=Rs.2500}}}}}}$

∴ The compound interest is Rs.2500.

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

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

$\dashrightarrow\small{\sf{Difference = 2500 - 2500}}$

$\dashrightarrow\small{\sf{Difference = 0}}$

$\longrightarrow\small{\underline{\boxed{\sf{Difference = 0}}}}$

∴ The difference between Compound interest and Simple interest is 0.

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

Lᴇᴀʀɴ Mᴏʀᴇ :

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

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

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

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

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

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

${\underline{\overline{\rule{200pt}{2pt}}}}$