
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
536.1k+ views
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.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Earth rotates from West to east ATrue BFalse class 6 social science CBSE

The easternmost longitude of India is A 97circ 25E class 6 social science CBSE

Write the given sentence in the passive voice Ann cant class 6 CBSE

Convert 1 foot into meters A030 meter B03048 meter-class-6-maths-CBSE

What is the LCM of 30 and 40 class 6 maths CBSE

Trending doubts
List some examples of Rabi and Kharif crops class 8 biology CBSE

What is the feminine gender of a stag class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Advantages and disadvantages of science
