Find the difference between the simple interest and the compound interest on ₹20000 at 10% p.a. compounded annually for 3 years.
Note- No spam or else 10 answers will be reported and plz show the whole method.
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Find the difference between the simple interest and the compound interest on ₹20000 at 10% p.a. compounded annually for 3 years.
Note- No spam or else 10 answers will be reported and plz show the whole method.
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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,
[tex]\boxed{\bold{Simple \: interest = \dfrac{P \times r \times t}{100}}}
[/tex]
Where,
p is principal, r is rate and t is time, period
[tex]\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{20000 \times 10 \times 3}{100} \\ \\ \end{gathered}
[/tex]
[tex]\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{600000}{100} \\ \\ \end{gathered}
[/tex]
[tex]\longrightarrow \purple{\boxed{\sf \bold{Simple \: interest = 6000}}\star}[/tex]
Thus,
Simple interest is ₹6000.
Interest is compounded annually.
So,
Compound interest = Amount - Principal
Or,
[tex]\boxed{\bold{Compound \: interest = \Bigg\{ P \bigg( 1 + \dfrac{r}{100} \bigg) ^{n} \Bigg\} - P}} [/tex]
Put the values :
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(1 + \dfrac{10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered} [/tex]
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg( \dfrac{100 + 10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered} [/tex]
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(\dfrac{110}{100} \bigg)^{3} \Bigg\} - 20000 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{20000 \times \dfrac{1331000}{1000000} \Bigg\} - 20000 \\ \\ \end{gathered} [/tex]
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times 1.331 \Bigg\} - 20000 \\ \\ \end{gathered} [/tex]
[tex]\begin{gathered} \sf \longrightarrow Compound \: interest = 26620 - 20000 \\ \\ \end{gathered} [/tex]
[tex]\begin{gathered} \longrightarrow \red{\boxed{\sf \bold{Compound \: interest = 6620}}\star} \\ \\ \end{gathered} [/tex]
Thus,
Compound interest is ₹6620
Now,
Difference = Compound interest - Simple interest
[tex]\sf \longrightarrow 6620 - 6000[/tex]
[tex]\sf \longrightarrow \bold{620}[/tex]
Therefore,
Difference is ₹620.
Answer:
₹620
Step-by-step explanation:
Answer: Difference is ₹620.