The difference between the compound interest and the simple interest on a principal sum of $₹24,000$ in $2$ years at same rate of interest is $₹60$. The rate of interest is:
To find the rate of interest at which the difference between the compound interest (CI) and simple interest (SI) for a principal of ₹24,000 over 2 years is ₹60, we need to use the formula for the difference between CI and SI. The difference over 2 years is given by:
\(CI - SI = \frac{P \cdot R^{2}}{100^{2}}\)
Here, \(CI - SI = ₹60\), \(P = ₹24,000\), and \(R\) is the rate of interest in percentage that we need to find.
Substitute the known values into the formula:
\(60 = \frac{24000 \cdot R^{2}}{100^{2}}\)
Which simplifies to:
\(60 = \frac{24000 \cdot R^{2}}{10000}\)
By multiplying both sides by 10000 to clear the fraction, we get:
\(60 \times 10000 = 24000 \cdot R^{2}\)
\(600000 = 24000 \cdot R^{2}\)
Now, divide both sides by 24000 to solve for \(R^{2}\):
\(R^{2} = \frac{600000}{24000}\)
\(R^{2} = 25\)
Taking the square root of both sides, we find \(R\):
\(R = \sqrt{25} = 5\%\)
Thus, the rate of interest is 5%.
Conclusion: The correct answer is \(5\%\).
Similar Questions
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Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
