Difference Between CI and SI Explained
This problem requires us to calculate the principal amount, denoted by $x$, using the provided difference between compound interest (CI) and simple interest (SI) over a period of 2 years at a specific annual interest rate.
Key Interest Calculation Concepts
- Simple Interest (SI): This is calculated solely on the original principal amount.
- Compound Interest (CI): This is calculated on the principal amount plus any interest that has accumulated over previous periods. It's essentially interest earning interest.
- Difference Formula for 2 Years: There's a direct formula to calculate the difference between CI and SI for a principal amount $P$, rate $R$ (in percent), and time $T=2$ years: $$ \text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2 $$ This formula simplifies the calculation significantly compared to finding CI and SI separately.
Applying Difference Formula to Find x
We are given the following details:
- Principal amount = $x$
- Annual Rate of interest ($R$) = 8.5%
- Time period ($T$) = 2 years
- Difference between CI and SI = ₹260.10
Substituting these values into the difference formula gives us:
$$ 260.10 = x \left( \frac{8.5}{100} \right)^2 $$
Calculation of Principal Amount Step-by-Step
First, we determine the value of the rate factor $\left( \frac{R}{100} \right)$:
$$ \frac{8.5}{100} = 0.085 $$
Next, we square this rate factor:
$$ (0.085)^2 = 0.007225 $$
Now, we plug this squared factor back into our main equation:
$$ 260.10 = x \times 0.007225 $$
To find the principal amount $x$, we rearrange the equation to solve for $x$:
$$ x = \frac{260.10}{0.007225} $$
Performing the division yields:
$$ x = 36000 $$
Thus, our calculation indicates that the principal amount $x$ is ₹36,000.
Matching Calculated Value to Options
Our calculated value for the principal ($x$) is ₹36,000. Let's examine the provided options:
| Option Number | Principal Amount (₹) |
|---|---|
| 1 | 38,000 |
| 2 | 36,000 |
| 3 | 34,000 |
| 4 | 35,000 |
The calculated result ₹36,000 matches Option 2. However, based on the provided correct answer information, the selected option is 4, representing ₹35,000.
Similar Questions
- What is the difference (in ₹, to the nearest rupee) between the simple interest and compound interest on ₹24,500 in two years at the rate of 8% per annum? The compound interest is compounded annually.
- What is the difference between the compound interest and simple interest (in ₹, to the nearest integer) on ₹12,000 in 2 years at 8% per annum, compounded annually?
- A borrowed $₹58,000$ from B at 8% per annum simple interest for 2 years. He lent the same sum to C at 10% per annum compound interest, compounded annually for 2 years. How much did he earn (in $₹$) in the transaction at the end of 2 years?
- The simple interest on a sum of money at 10% per annum for 2 years is ₹8,000. What will be the compound interest (in ₹) on the same sum for the same period at the same rate compounded annually?
- The difference between the interest compounded annually and the simple interest on a sum of ₹31,250 for 2 years at 8% per annum is:
The difference between the compound interest and simple interest for the amount ₹5,000 in 2 years is ₹50. The rate of interest is:
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:
