(a) Find the compound interest on Rs.96000 for 2 years 3 months at 5% per annum interest being compounded annually.
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(a) Find the compound interest on Rs.96000 for 2 years 3 months at 5% per annum interest being compounded annually.
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Answer:
✠
Given:—
Principal = 96000 rupees
Time = 2 years 3 months
Rate = 5%
\maltese{\underline{\textbf{\textsf{To\:Find:—}}}}✠
ToFind:—
Find the compound interest.
\maltese{\underline{\textbf{\textsf{Using\:Formula:—}}}}✠
UsingFormula:—
Formula for finding the amount
\bigstar{\boxed{\bold{a = p {(1 + ( \frac{r}{100}) }^{n}}}}★
a=p(1+(
100
r
)
n
Formula for finding the Compound interest
\bigstar{\boxed{\bold{compound \: interest = amount - principal}}}★
compoundinterest=amount−principal
\maltese{\underline{\textbf{\textsf{Solution:—}}}}✠
Solution:—
\bigstar★ According to the question—
\begin{gathered} {\longrightarrow}{\tt{a = 96000 {(1 + \frac{5}{100} }^{2} (1 + \frac{( \frac{1}{4} \times 1 \cancel0) }{10 \cancel0}}} \\ \\ {\longrightarrow}{\tt{a = 96000 {(1 + \frac{1}{20} ) }^{2} (1 + \frac{1}{40}}} \\ \\ {\longrightarrow} {\tt{a = 96000 { (\frac{21}{20}) }^{2} ( \frac{41}{40})}} \\ \\ {\longrightarrow}{\tt{a = 96000 \times \frac{441}{400} \times \frac{41}{40}}} \\ \\ {\longrightarrow}{\tt{a = 144648 \: rupees}}\end{gathered}
⟶a=96000(1+
100
5
2
(1+
10
0
(
4
1
×1
0
)
⟶a=96000(1+
20
1
)
2
(1+
40
1
⟶a=96000(
20
21
)
2
(
40
41
)
⟶a=96000×
400
441
×
40
41
⟶a=144648rupees
Hence,the amount will be 144648 rupees.
\begin{gathered} {\longrightarrow}{\tt{compound \: interest = 144648 - 96000}} \\ \\ {\longrightarrow}{\tt{compound \: interest = 48648 \: rupees}}\end{gathered}
⟶compoundinterest=144648−96000
⟶compoundinterest=48648rupees
\maltese{\underline{\textbf{\textsf{Therefore:—}}}}✠
Therefore:—
Amount = 144648 rupees
Compound Interest = 48648 rupees