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
Amar borrowed Rs. 10000 from Sachin at simple interest. After 4 years, Sachin received Rs. 5000 more than the amount given to Amar on loan. Find the rate of interest.
Simple interest accrued on the amount of Rs.14,000 is Rs. 1260 at the rate of 3 % per annum for t years. What would be the compound interest accrued on the same amount for the same years at 10 % per annum compounded annually?
Rishu deposited an amount of Rs. 950 at Compound Interest. The amount gets doubled of itself after 4 years. What will be the amount after 12 years?
Which of the following schemes of computing interest yields the maximum interest for a year?
On a certain sum, rate of interest per annum for the first two years is 4%. The rate of interest for next four years is 6% and for the next three years is 8%. If total simple interest earned at the end of 9 years is ₹ 1120, then the sum is:
