Question

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

Answer 1

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.