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Answers
Answer:
Answer:
Difference is ₹620.
Step-by-step explanation:
Given :-
Principal is ₹20000.
Rate of interest is 10%.
Time period is 3 years.
To find :-
Difference between the simple interest and compound interest.
Solution :-
For difference first we will find simple interest and compound interest.
So,
We know,
\boxed{\bold{Simple \: interest = \dfrac{P \times r \times t}{100}}}
Simpleinterest=
100
P×r×t
Where,
P is principal, r is rate of interest and t is time period.
Put all values :
\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{20000 \times 10 \times 3}{100} \\ \\ \end{gathered}
⟶Simpleinterest=
100
20000×10×3
\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{600000}{100} \\ \\ \end{gathered}
⟶Simpleinterest=
100
600000
\longrightarrow \purple{\boxed{\sf \bold{Simple \: interest = 6000}}\star}⟶
Simpleinterest=6000
⋆
Thus,
Simple interest is ₹6000.
Interest is compounded annually.
So,
Compound interest = Amount - Principal
Or,
\boxed{\bold{Compound \: interest = \Bigg\{ P \bigg( 1 + \dfrac{r}{100} \bigg) ^{n} \Bigg\} - P}}
Compoundinterest={P(1+
100
r
)
n
}−P
Put the values :
\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(1 + \dfrac{10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered}
⟶Compoundinterest={20000×(1+
100
10
)
3
}−20000
\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg( \dfrac{100 + 10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered}
⟶Compoundinterest={20000×(
100
100+10
)
3
}−20000
\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(\dfrac{110}{100} \bigg)^{3} \Bigg\} - 20000 \\ \\ \end{gathered}
⟶Compoundinterest={20000×(
100
110
)
3
}−20000
\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{20000 \times \dfrac{1331000}{1000000} \Bigg\} - 20000 \\ \\ \end{gathered}
⟶Compoundinterest={20000×
1000000
1331000
}−20000
\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times 1.331 \Bigg\} - 20000 \\ \\ \end{gathered}
⟶Compoundinterest={20000×1.331}−20000
\begin{gathered} \sf \longrightarrow Compound \: interest = 26620 - 20000 \\ \\ \end{gathered}
⟶Compoundinterest=26620−20000
\begin{gathered} \longrightarrow \red{\boxed{\sf \bold{Compound \: interest = 6620}}\star} \\ \\ \end{gathered}
⟶
Compoundinterest=6620
⋆
Thus,
Compound interest is ₹6620
Now,
Difference = Compound interest - Simple interest
\sf \longrightarrow 6620 - 6000⟶6620−6000
\sf \longrightarrow \bold{620}⟶620
Therefore,
Difference is ₹620.