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
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
- A sum of money was lent on compound interest. It became ₹500 at the end of the first year and ₹550 at the end of second year. Find the rate of compound interest per annum.
- Simple interest on a sum of money, at $5\%$ per annum for 2 years, is ₹50. The compound interest on the same sum for the same period at the same interest rate is:
- If a sum on compound interest becomes 4 times in 3 years, then with the same interest rate, the sum will become 64 times in:
- If the difference between the compound interest and the simple interest on a certain sum of money at 8 % p.a. for 2 years is ₹240, then the sum of money is:
- The compound interest on a sum of ₹7,500 for 2 years at 4 % p.a. is
Important Questions from Simple and Compound Intrest
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
- Amit invested the same sum at simple and compound interest (compounded annually) for 2 years at 4% per annum. The difference between the compound interest and the simple interest is ₹47. Find the sum (in ₹) invested in each case.
- Amit invested equal amounts at simple interest and compound interest, compounded annually, for 2 years at the same rate of 4% per annum. In the end, he found a difference of ₹53 between the two interests earned. What was the amount (in ₹) invested in each case?
