# In what time will Rs.7500 amount to Rs.8625, if simple interest is reckoned at $7\dfrac{1}{2}$% per annum?

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Hint – In this question the principal amount is given to us and we need to tell the time in which this amount gets hiked to Rs.7500 if interest is reckoned at $7\dfrac{1}{2}$% per annum. Use the direct formula for Simple interest to calculate the time in which the principal value hikes up.

Complete step-by-step answer:

Given data

Principal amount (P) $ = Rs.7500$

Amount (A) after interest $ = Rs.8625$

Rate (r) of interest $7\dfrac{1}{2}$ % per annum

$ \Rightarrow r = \dfrac{{\left( {7 \times 2} \right) + 1}}{2} = \dfrac{{15}}{2}$ %.

Now as we know that the formula to calculate simple interest (S.I) is

$ \Rightarrow S.I = \dfrac{{P.r.t}}{{100}}$ …………………………. (1)

Where t = time in years.

r = rate of interest.

P = principal amount.

And the amount after simple interest is the sum of principal amount and simple interest.

$ \Rightarrow A = P + S.I$

$ \Rightarrow S.I = A - P = 8625 - 7500 = 1125\;Rs.$

Now substitute all the values in equation (1) we have,

$ \Rightarrow 1125 = \dfrac{{7500 \times \dfrac{{15}}{2} \times t}}{{100}}$

Now simplify the above equation we have,

$ \Rightarrow t = \dfrac{{112500 \times 2}}{{7500 \times 15}} = \dfrac{{15 \times 2}}{{15}} = 2$ years.

So, in 2 years Rs.7500 becomes Rs.8625.

So, this is the required answer.

Note – Whenever we face such types of problems the key point is simply to have a good gist of the direct basic formula for Simple Interest, an interest compounded annually is different from a simple interest calculated annually. Use this concept to reach the solution.

Complete step-by-step answer:

Given data

Principal amount (P) $ = Rs.7500$

Amount (A) after interest $ = Rs.8625$

Rate (r) of interest $7\dfrac{1}{2}$ % per annum

$ \Rightarrow r = \dfrac{{\left( {7 \times 2} \right) + 1}}{2} = \dfrac{{15}}{2}$ %.

Now as we know that the formula to calculate simple interest (S.I) is

$ \Rightarrow S.I = \dfrac{{P.r.t}}{{100}}$ …………………………. (1)

Where t = time in years.

r = rate of interest.

P = principal amount.

And the amount after simple interest is the sum of principal amount and simple interest.

$ \Rightarrow A = P + S.I$

$ \Rightarrow S.I = A - P = 8625 - 7500 = 1125\;Rs.$

Now substitute all the values in equation (1) we have,

$ \Rightarrow 1125 = \dfrac{{7500 \times \dfrac{{15}}{2} \times t}}{{100}}$

Now simplify the above equation we have,

$ \Rightarrow t = \dfrac{{112500 \times 2}}{{7500 \times 15}} = \dfrac{{15 \times 2}}{{15}} = 2$ years.

So, in 2 years Rs.7500 becomes Rs.8625.

So, this is the required answer.

Note – Whenever we face such types of problems the key point is simply to have a good gist of the direct basic formula for Simple Interest, an interest compounded annually is different from a simple interest calculated annually. Use this concept to reach the solution.

Last updated date: 23rd Sep 2023

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