Find the Amount and the Compound Interest on Rs 125000 for 1 1/2 years at 4% per annum compounded half-yearly.
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Answers
Answer:
Solution−
Given that,
Principal, P = Rs 125000
Rate of interest, r = 4 % per annum compounded half yearly.
Time, n = 1 1/2 years = 3/2 years
We know,
Amount on a certain sum of money of Rs P invested at the rate of r % per annum compounded half yearly for n years is given by
\begin{gathered}\boxed{\sf{ \: \: Amount \: = \: P \: {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }} \\ \end{gathered}
Amount=P[1+
200
r
]
2n
On substituting the values, we get
\begin{gathered}\rm \: Amount \: = \: 125000 {\bigg[1 + \dfrac{4}{200} \bigg]}^{3} \\ \end{gathered}
Amount=125000[1+
200
4
]
3
\begin{gathered}\rm \: Amount \: = \: 125000 {\bigg[1 + \dfrac{2}{100} \bigg]}^{3} \\ \end{gathered}
Amount=125000[1+
100
2
]
3
\begin{gathered}\rm \: Amount \: = \: 125000 {\bigg[ \dfrac{100 + 2}{100} \bigg]}^{3} \\ \end{gathered}
Amount=125000[
100
100+2
]
3
\begin{gathered}\rm \: Amount \: = \: 125000 {\bigg[ \dfrac{102}{100} \bigg]}^{3} \\ \end{gathered}
Amount=125000[
100
102
]
3
\begin{gathered}\rm \: Amount \: = \: 125000 {\bigg[ 1.02 \bigg]}^{3} \\ \end{gathered}
Amount=125000[1.02]
3
\begin{gathered}\rm\implies \:Amount \: = \: 132651 \\ \end{gathered}
⟹Amount=132651
We know,
\begin{gathered}\rm \: Compound\:Interest \: = \: Amount \: - \: P \: \\ \end{gathered}
CompoundInterest=Amount−P
\begin{gathered}\rm \: = \: 132651 - 125000 \\ \end{gathered}
=132651−125000
\begin{gathered}\rm \: = \: 7651 \\ \end{gathered}
=7651
So,
\begin{gathered}\rm\implies \:Compound\:Interest \: = \: 7651 \\ \end{gathered}
⟹CompoundInterest=7651
Hence,
Amount = Rs 132651
and
Compound Interest = Rs 7651
hope you get help from it
answered by Answer Queen