Answer
Verified
377.4k+ views
Hint: This is a problem based on compound interest. We are given the rate of interest, time period and the amount that is interest and principal together. We have to find the principal sum. That is the amount that was invested in this compound interest. So we will use the formula of compound interest and amount calculation to solve this problem.
Formula used:
\[A = p{\left[ {1 + \dfrac{R}{{100}}} \right]^t}\]
Where,
$A$ is the amount
$P$ is the principal sum
$R$ is the rate of interest per annum
$t$ is the time period in years
Complete step by step solution:
Given that, a sum of money amounts to Rs.66836.70 in 2 years at 3% p.a.
That is the amount after adding the interest is given . we have to find the principal. So we will use the formula above.
\[A = p{\left[ {1 + \dfrac{R}{{100}}} \right]^t}\]
Now substitute the given data,
\[66836.70 = p{\left[ {1 + \dfrac{3}{{100}}} \right]^2}\]
Now taking the LCM in the bracket,
\[66836.70 = p{\left[ {\dfrac{{103}}{{100}}} \right]^2}\]
\[\Rightarrow 66836.70 = p\left[ {\dfrac{{{{103}^2}}}{{{{100}^2}}}} \right]\]
On cross multiplying we get,
\[p = \dfrac{{66836.70 \times {{100}^2}}}{{{{103}^2}}}\]
Taking the squares,
\[p = \dfrac{{66836.70 \times {{100}^2}}}{{10609}}\]
On dividing by 10609 we get and also taking the square of 100,
\[p = 6.3 \times 10000\]
On multiplying the decimal will be removed,
\[p = 63000\]
This is the principal sum invested Rs.63000.
Note:
Note that they have given all the required data simply using the formula is enough. But the time period should be in years if it is not then do make it because the rate is per cent per annum.
If asked for the interest then we will subtract the principal from the amount sum.
Formula used:
\[A = p{\left[ {1 + \dfrac{R}{{100}}} \right]^t}\]
Where,
$A$ is the amount
$P$ is the principal sum
$R$ is the rate of interest per annum
$t$ is the time period in years
Complete step by step solution:
Given that, a sum of money amounts to Rs.66836.70 in 2 years at 3% p.a.
That is the amount after adding the interest is given . we have to find the principal. So we will use the formula above.
\[A = p{\left[ {1 + \dfrac{R}{{100}}} \right]^t}\]
Now substitute the given data,
\[66836.70 = p{\left[ {1 + \dfrac{3}{{100}}} \right]^2}\]
Now taking the LCM in the bracket,
\[66836.70 = p{\left[ {\dfrac{{103}}{{100}}} \right]^2}\]
\[\Rightarrow 66836.70 = p\left[ {\dfrac{{{{103}^2}}}{{{{100}^2}}}} \right]\]
On cross multiplying we get,
\[p = \dfrac{{66836.70 \times {{100}^2}}}{{{{103}^2}}}\]
Taking the squares,
\[p = \dfrac{{66836.70 \times {{100}^2}}}{{10609}}\]
On dividing by 10609 we get and also taking the square of 100,
\[p = 6.3 \times 10000\]
On multiplying the decimal will be removed,
\[p = 63000\]
This is the principal sum invested Rs.63000.
Note:
Note that they have given all the required data simply using the formula is enough. But the time period should be in years if it is not then do make it because the rate is per cent per annum.
If asked for the interest then we will subtract the principal from the amount sum.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE