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
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
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Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- 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:
