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# You invested Rs.1500 and received Rs.5000 after three years. What had been the interest rate?(A) $111.11\%$(B) $222.22\%$(C) $333.33\%$(D) $77.77\%$

Last updated date: 19th Jul 2024
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Hint: We are given that when we invested an amount Rs.1500, we received an amount of Rs.5000 after three years. We are asked to find the interest rate for the given values. We will use the formula of simple interest, which is, $S.I=\dfrac{P\times R\times T}{100}$. We will substitute the values in the formula and solve it to find the value of the rate of interest. Hence, we will have the required value as asked in the question.

Complete step by step answer:
According to the given question, we are given the principal amount, which is, Rs.1500 which is invested for three years after which we get the amount as Rs.5000. we are asked in the question to find the rate of interest for the same.
We will first write down the given,
The principal amount, P = Rs.1500
Time period, T = 3 years
Amount received after the tenure = Rs.5000
Here, we will use the simple interest formula to find the rate of interest, R, we have,
$S.I=\dfrac{P\times R\times T}{100}$
We will now substitute the values in the above expression, we get,
$\Rightarrow 5000=\dfrac{1500\times R\times 3}{100}$
Now, we will cross multiply the 100 and we get,
$\Rightarrow 5000\times 100=1500\times R\times 3$
Solving further for R, we get,
$\Rightarrow 500000=4500R$
Now, writing the expression in terms of R, we get,
$\Rightarrow R=\dfrac{500000}{4500}$
Cancelling out the common zeroes and we have,
$\Rightarrow R=\dfrac{5000}{45}$
Dividing the fraction, we get the value of R as,
$\Rightarrow R=111.11\%$
Therefore, the rate of interest is (A) $111.11\%$

So, the correct answer is “Option A”.

Note: The contrast as to when to use simple interest and when to use compound interest should be made familiar and not mixed up. Simple interest in simple words is based on the principal amount whereas compound interest is based on principal amount and the interest that accumulates. The formula of the compound interest is as follows,
$A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}$