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# The interest on a certain sum of money is Rs. $1480$ in $2$ years and at $10$ percent per year.Find the sum of money (in Rs.)

Last updated date: 24th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
Difference between simple interest and compound interest is that simple interest based on the principal of a deposit or a loan where compound interest based on the principal and interest that accumulates in every period of time.
We can use a direct formula of simple interest.

Since the sum of the money on a certain interest and percentage per year is given in the question
Thus, the given problem is simple interest problem
As we know the formula for the simple interest is $I = \dfrac{{PNR}}{{100}}$
Where $P$ is the initial principal amount, $R$ is the annual rate of interest and $N$ is the length of time you invest or borrow
Also $I$ is the interest earned after $N$ years
Here from the given question, $I$ = Rs. $1480$ (interest earned after 2 years)
$N$ = $2$ years (time), $R$ = $10$ % (annual rate of interest)
Thus, the only unknown value is $P$ we can find it use the simple interest formula
That is $I = \dfrac{{PNR}}{{100}}$ $\Rightarrow 1480 = \dfrac{{P \times 2 \times 10}}{{100}}$ (substituting each and every known value)
Now cross multiplying we get $P \times 2 \times 10 = 100 \times 1480$
On right hand multiplying $100 \times 1480$ we get $148000$ and applying in the above equation
We get $P \times 2 \times 10 = 148000$
Now by cancelling $10$ on both sides we get $P \times 2 = 14800$
And again cancelling $2$ on both sides we get $P = 7400$
Hence, we get $P = 7400$ is the initial principal amount that is invested.

Note: Here $P$ is the initial principal amount is the unknown value so we find it.
If suppose any other than $P$ is an unknown, we are able to find simple interest using the formula and methods as above.