Find the compound interest on 10000 at 10% per annum for 2.2 years compounded anually
Answers
Answer:
What is the amount on a principal of Rs 10000 for 2 years at 10% per annum when interest is compounded annually?
Principal = Rs. 10000; Rate = 2% per half-year; Time = 2 years = 4 half-years. Amount == Rs. 10824.32.
GIVEN :-
Principal ( P ) = Rs. 10000
Amount ( A ) = Rs. 12000
Rate ( R ) = 12% Per annum.
TO FIND :-
The time ( n ).
SOLUTION :-
As we know that,
\begin{gathered} \implies \displaystyle \sf \:Amount = P\bigg\lgroup 1 + \dfrac{R}{100}\bigg\rgroup ^{n} \\ \end{gathered}
⟹Amount=P
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1+
100
R
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n
\begin{gathered}\implies \displaystyle \sf \:12000 = 10000 \bigg \lgroup1 + \frac{12}{100} \bigg \rgroup ^{n} \\ \end{gathered}
⟹12000=10000
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1+
100
12
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n
\begin{gathered}\implies \displaystyle \sf \: \frac{12000}{10000} = \bigg \lgroup \frac{100 + 12}{100} \bigg \rgroup ^{n} \\ \end{gathered}
⟹
10000
12000
=
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100
100+12
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n
\begin{gathered}\implies \displaystyle \sf \: \frac{12}{10} = \bigg \lgroup \frac{112}{100} \bigg \rgroup ^{n} \\ \end{gathered}
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10
12
=
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100
112
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n
\begin{gathered}\implies \displaystyle \sf \: \frac{6}{5} = \bigg \lgroup \frac{28}{25} \bigg \rgroup ^{n} \\ \end{gathered}
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5
6
=
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25
28
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n
\begin{gathered}\implies \displaystyle \sf \: (1.12) ^{1.6} = {(1.12)} ^{ n} \\ \end{gathered}
⟹(1.12)
1.6
=(1.12)
n
\implies \underline{ \boxed{ \displaystyle \sf \:n = 1.6 \: years}}⟹
n=1.6years