Finding the Principal Amount Using Interest Difference
The problem asks us to find the principal amount (P) given the difference between compound interest (CI) and simple interest (SI) over 2 years is ₹25, at an annual interest rate (R) of 5%.
Understanding the Interest Difference Formula
For a period of 2 years, the difference between compound interest and simple interest is calculated using the formula:
Difference = $P \times \left(\frac{R}{100}\right)^2$
Where:
- P = Principal Amount
- R = Annual Interest Rate (%)
Applying the Formula
We are given:
- Difference = ₹25
- R = 5%
Substitute the known values into the formula:
$25 = P \times \left(\frac{5}{100}\right)^2$
Calculating the Principal Amount
- Simplify the fraction: $\frac{5}{100} = \frac{1}{20}$
- Square the fraction: $\left(\frac{1}{20}\right)^2 = \frac{1}{400}$
- Rewrite the equation: $25 = P \times \frac{1}{400}$
- Solve for P: $P = 25 \times 400$
- Calculate the final value: $P = 10000$
Therefore, the principal amount is ₹10,000.
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).
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
- 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 ₹______.
