Question

find the simple interest an compound interest on 5000rs at rate of 10% pa for 3 years.

Answer 1

Answer:

1500

Step-by-step explanation:

principal=₹5000

Time=3years

rate=10%

sp= 5000×3×10/100

sp=1500

amount=principal + simple interest

=5000 + 1500

=₹6500

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Answer 2

Answer:

Given :

• → Principle = Rs.5000
• → Rate = 10%
• → Time = 3 years.

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

To Find :

• → Simple Interest
• → Amount
• → Compound Interest

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

Using Formulas :

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

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

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

✏ Where :-

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

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

Solution :

✏ Finding Simple Interest :-

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

$\dashrightarrow\small{\sf{ S.I = \dfrac{5000\times 10\times 3}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{5000\times 30}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \dfrac{150000}{100}}}$

$\dashrightarrow\small{\sf{ S.I = \cancel{\dfrac{150000}{100}}}}$

$\dashrightarrow\small{\sf{ S.I = Rs.1500}}$

$\bigstar \: \small{\purple{\underline{\boxed{\sf{ S.I = Rs.1500}}}}}$

∴ The simple interest is Rs.1500.

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✏ Finding compound interest but first we have to calculate amount :-

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

$\dashrightarrow\small{\sf{Amount= 5000\bigg(1 + \dfrac{10}{100} \bigg)^{3}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{(1 \times 100)(10 \times 1)}{100} \bigg)^{3}}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{100 + 10}{100} \bigg)^{3}}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{110}{100} \bigg)^{3}}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg( \cancel\dfrac{110}{100} \bigg)^{3}}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{11}{10} \bigg)^{3} }}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} \bigg)}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000\bigg(\dfrac{1331}{1000}\bigg)}}}}$

${\dashrightarrow{\small{\sf{Amount= 5000 \times \dfrac{1331}{1000}}}}}$

${\dashrightarrow{\small{\sf{Amount= \cancel{5000}\times \dfrac{1331}{\cancel{1000}}}}}}$

${\dashrightarrow{\small{\sf{Amount= 5 \times 1331}}}}$

${\dashrightarrow{\small{\sf{Amount= Rs.6655}}}}$

${\dashrightarrow{\small{\purple{\underline{\boxed{\sf{Amount= Rs.6655}}}}}}}$

∴ The Amount is Rs.6655.

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✏ Now, calculating the compound interest

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

$\longrightarrow\small{\sf{{C.I=6655- 5000}}}$

$\longrightarrow\small{\purple{\underline{\boxed{\sf{{C.I=Rs.1655}}}}}}$

∴ The compound interest is Rs.1655.

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

Learn More :

☼ Principal:

→ Money which is taken or given in the form of loan. That's called the principal. It is denoted by P.

☼ Time:

The period for which the loan is taken or given is called time. It is expressed by T or t.

☼ Rate of Interest

→ The rate at which interest is charged or paid is called interest rate. It is denoted by r or R.

☼ Interest:

→ In addition to the principal amount, which is refunded, interest is paid. It is denoted by I.

☼ Amount :

→ For example, money taken is called principal and money returned is called compound.

$\rule{150}1.5$

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

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

$\longrightarrow\small{\underline{\boxed{\sf{\green{Amount = Principle + Interest}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\green{ Principle=Amount - Interest }}}}}$

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

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

$\longrightarrow\small{\underline{\boxed{\sf{\green{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}}}$

$\longrightarrow\small{\underline{\boxed{\sf{\green{Time = \dfrac{Simple \: Interest \times 100}{Principle \times Rate}}}}}}$

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