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
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?
An electric bulb was bought at Rs. 4200 Its value depreciates at the rate of 8% per annum Its value after one year will be:
What is the amount of money invested after 4 years at the rate of simple interest rate of 13% per annum invested at 4,950 rupees. (In rupees)
A certain sum of money amounts to \(\frac{3}{2}\) of itself in 2 years applying simple interest. Find the rate of simple interest per annum.
A sum of Rs. 2000 will become Rs. 2400 in 12 months at some rate of simple interest. Find the rate of interest per annum.
