Difference between the compound interest (compounded annually) and simple interest on a sum of ₹ 4900 at a certain rate for 2 years is ₹ 100. Find the rate.
Question
Difference between the compound interest (compounded annually) and simple interest on a sum of ₹ 4900 at a certain rate for 2 years is ₹ 100. Find the rate.
Solution
Sure, let's solve this step by step.
Given: Principal (P) = ₹ 4900 Time (T) = 2 years Difference between Compound Interest (CI) and Simple Interest (SI) = ₹ 100
We know that the difference between CI and SI for 2 years is given by the formula:
CI - SI = P*(R/100)^2
Where R is the rate of interest.
We can substitute the given values into this formula to find the rate of interest.
100 = 4900*(R/100)^2
Solving this equation for R gives:
R^2 = (100 * 100 * 2) / 4900
R^2 = 400 / 49
Taking the square root of both sides to solve for R gives:
R = √(400 / 49)
R = 20 / 7
So, the rate of interest is 20/7 = 2.8571 or approximately 2.86% per annum.
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