# Find the compound interest paid when a sum of Rs.10,000 is invested for 1 year and 3 months at 17/2% per annum compounded annually

Last updated date: 21st Mar 2023

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Answer

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Hint-First,find out the amount and calculate the simple interest and then calculate the compound interest.

Given that the initial investment =Principal=Rs.10,000

Time period is given as 1 year and 3 months=15months

So, for first year let us calculate the compound interest and then calculate the simple interest for the remaining 3 months and find the compound interest

So, the amount at the end of 1 year=

Formula =$P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$

$\begin{gathered}

10000{\left( {1 + \dfrac{{\dfrac{{17}}{2}}}{{100}}} \right)^1} = 10000{\left( {1 + \dfrac{{17}}{{200}}} \right)^1} \\

= 10000 \times \dfrac{{217}}{{200}} \\

= Rs.10850 \\

\end{gathered} $

So, the amount at the end of 1 year=Rs.10850

Now, let us calculate the simple interest for the remaining 3 months

SI=$\dfrac{{PTR}}{{100}}$

Let us substitute the values here,

We have Principal=Rs.10,850

And time period =3 months=$\dfrac{3}{{12}}$ ,

Rate of interest=$\dfrac{{17}}{2}$

So, we get SI=$\dfrac{{10850 \times \dfrac{3}{{12}} \times \dfrac{{17}}{2}}}{{100}}$ =Rs.230.56

So, the total amount will now be equal to

=Rs.10850+230.56

=Rs.11080.56

Now this is the Amount , but we are supposed to find the compound interest,

So, we can write Compound interest=Amount-Principal

=11080.65-10000

So, compound Interest=Rs.1080.56

Note -Here, we have calculated the amount for 1 year and then we have calculated the simple interest for 3 months and added them up, we can also take the total time period as 15 months (1.25 years) and solve it.

Given that the initial investment =Principal=Rs.10,000

Time period is given as 1 year and 3 months=15months

So, for first year let us calculate the compound interest and then calculate the simple interest for the remaining 3 months and find the compound interest

So, the amount at the end of 1 year=

Formula =$P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$

$\begin{gathered}

10000{\left( {1 + \dfrac{{\dfrac{{17}}{2}}}{{100}}} \right)^1} = 10000{\left( {1 + \dfrac{{17}}{{200}}} \right)^1} \\

= 10000 \times \dfrac{{217}}{{200}} \\

= Rs.10850 \\

\end{gathered} $

So, the amount at the end of 1 year=Rs.10850

Now, let us calculate the simple interest for the remaining 3 months

SI=$\dfrac{{PTR}}{{100}}$

Let us substitute the values here,

We have Principal=Rs.10,850

And time period =3 months=$\dfrac{3}{{12}}$ ,

Rate of interest=$\dfrac{{17}}{2}$

So, we get SI=$\dfrac{{10850 \times \dfrac{3}{{12}} \times \dfrac{{17}}{2}}}{{100}}$ =Rs.230.56

So, the total amount will now be equal to

=Rs.10850+230.56

=Rs.11080.56

Now this is the Amount , but we are supposed to find the compound interest,

So, we can write Compound interest=Amount-Principal

=11080.65-10000

So, compound Interest=Rs.1080.56

Note -Here, we have calculated the amount for 1 year and then we have calculated the simple interest for 3 months and added them up, we can also take the total time period as 15 months (1.25 years) and solve it.

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