Question

What sum of money will amount to Rs \[4230\] in \[2.5\] years at \[7\% \] \[p.a.\] \[S.I.?\]

Answer 1

Hint: To solve this question first we take the variable as a sum of money. Then we use the formula of simple interest and make two-equations from the formula of simple interest and then from those two equations we are able to find the sum of money.

Complete step-by-step solution:
Given,
\[amount = 4230\]
\[time (T) = 2.5years\]
\[{\text{rate}} {\text{of}} {\text{interest (R) = }}7\% \] this interest is per annum
To find,
Sum of the amount ( principal amount)
Formula used:
\[S.I. = (\dfrac{\text{principal amount} \times \text{time} \times \text{rate of interest}}{{100}})\]
\[S.I. = \dfrac{{P \times T \times R}}{{100}}\]
\[S.I. = \text{Amount} - \text{ Principal amount}\]
Let, the value of principal amount is
\[ \Rightarrow P = x\]
On putting the values in the formula
\[S.I. = \text{Amount} - \text{Principal amount}\]
\[S.I. = 4230 - x\] …. (i)
On putting all the value in formula
\[S.I. = \dfrac{{P \times T \times R}}{{100}}\]
\[S.I. = \dfrac{{x \times 2.5 \times 7}}{{100}}\] …. (ii)
Putting the value of \[S.I.\] in equation (ii) from the equation (i)
\[4320 - x = \dfrac{{x \times 2.5 \times 7}}{{100}}\]
On taking \[100\] to another side that will go in multiplication
\[100 \times (4320 - x) = x \times 2.5 \times 7\]
On solving further
\[432000 - x \times 100 = x \times 17.5\]
On taking \[100x\] to another side \[ - 100x\] will changed to \[100x\]
\[432000 = x17.5 + x100\]
On adding both the terms of \[x\]. We get,
\[432000 = 117.5x\]
Taking \[117.5\] to another side
\[\dfrac{{432000}}{{117.5}} = x\]
On rearranging. We get,
\[x = \dfrac{{432000}}{{117.5}}\]
\[x = 3600\]
The value of sum of amount with \[amount = 4230\], \[time = 2.5years\], \[{\text{rate}} {\text{of}} {\text{interest = }}7\% \] is
\[ \Rightarrow \text{principal amount} = 3600\]
Additional information:
Simple interest: Simple interest is used to calculate the interest of a particular time by using the formula of interest.
\[A = P(1 + rt)\]
Here,
\[A\] is the total amount after a particular time interval
\[P\] is the principal amount
\[r\] is the rate of interest per annum
\[t\] is the time period.
Compound interest: compound interest is an interest that is applied on principal amount as well as on previous interest also.
\[A = P{(1 + \dfrac{r}{n})^{nt}}\]
\[A\] is the total amount after a particular time interval
\[P\] is the principal amount
\[r\] is the rate of interest per annum
\[t\] is the time period.
\[n\] is the number of times the interest is applied.

Note: Here, we have to use the concept of how we find the simple interest. And must know the relation between simple interest, principal amount, and total amount. One direct formula for calculating the simple interest and use both the equation to find the principal amount and the simple interest.