To find the rate of interest per annum, given the difference between compound interest and simple interest for 2 years, we can use the following formulas:
Simple Interest (SI) for 2 years is given by:
\(SI = \frac{P \cdot R \cdot T}{100}\)
where:
- \(P\) is the principal amount,
- \(R\) is the rate of interest per annum, and
- \(T\) is the time period in years.
Compound Interest (CI) for 2 years is given by:
\(CI = P \left(1 + \frac{R}{100}\right)^2 - P\)
The difference between CI and SI for 2 years can be approximated (for small values of \(R\)) by:
\(CI - SI = \frac{P \cdot R^2}{100^2}\)
Given:
- \(P = 25,000\) Rs.
- \(CI - SI = 250\) Rs.
- \(T = 2\) years
Substitute the known values into the difference formula:
\(250 = \frac{25000 \cdot R^2}{100^2}\)
Simplifying, we have:
\(250 = \frac{25000 \cdot R^2}{10000}\)
\(250 \times 10000 = 25000 \times R^2\)
\(R^2 = \frac{2500000}{25000}\)
\(R^2 = 100\)
Taking the square root on both sides gives:
\(R = \sqrt{100} = 10\)
Thus, the rate of interest per annum is 10%.
Therefore, the correct answer is Option: 10.
Important Questions from Interest
- Increase in Debt-Equity ratio in a firm __________ to equity holders.
The difference between the compound interest and simple interest on a certain amount at 5%per annum for 2 years is Rs. 15.The principal amount is equal to :
Dhoni invested Rs 22000 at 12% simple interest per annum and Rs 15000 at 10% compound interest per annum, then find the total amount earned by him at the end of 2 years.
The difference between the compound interest and the simple interest on a sum of Rs. 8,000 for 2 years at the rate of 5% p.a. is:
Three years ago, the value of a flat was Rs. 65,00,000. Its value depreciated at the rate of 5%, 4% and 3% at the end of the first, the second and the third year, respectively. What is its present value?
