Finding the Interest Rate
The problem asks for the annual interest rate (R) given the principal amount (P), time period (T), and the difference between compound interest (CI) and simple interest (SI) for that period.
Given Information:
- Principal Amount, P = ₹15,000
- Time Period, T = 2 years
- Difference between CI and SI = ₹24
Formula for CI - SI Difference (2 years):
For a period of 2 years, the difference between compound interest and simple interest is given by the formula:
$ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 $
Where:
- P = Principal Amount
- R = Annual Interest Rate (in percent)
Calculation Steps:
- Substitute the given values into the formula: $ 24 = 15000 \left( \frac{R}{100} \right)^2 $
- Rearrange the formula to solve for $ \left( \frac{R}{100} \right)^2 $: $ \left( \frac{R}{100} \right)^2 = \frac{24}{15000} $
- Simplify the fraction: $ \left( \frac{R}{100} \right)^2 = \frac{8}{5000} = \frac{1}{625} $
- Take the square root of both sides to find $ \frac{R}{100} $: $ \frac{R}{100} = \sqrt{\frac{1}{625}} $ $ \frac{R}{100} = \frac{1}{25} $
- Solve for R: $ R = \frac{100}{25} $ $ R = 4 $
Therefore, the rate of interest per annum is 4%.
Similar Questions
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Important Questions from Simple and Compound Intrest
- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 16% per annum is ₹797. Find the sum (rounded off to the nearest integer).
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- The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 10% per annum is $₹407$. Find the sum [rounded off to the nearest integer].
The difference between the simple interest and the compound interest, compounded annually, on a certain sum of money for 2 years at 17% per annum is ₹967. Find the sum [rounded off to the nearest integer].
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
