Calculating Compound Interest from Simple Interest Details
This problem asks us to find the compound interest (CI) given information about the simple interest (SI) on a sum of money. We are given the SI amount, the interest rate, and the time period. We need to use this information to first find the principal amount and then calculate the compound interest for the same principal, rate, and time.
Step 1: Finding the Principal Amount
We know the formula for simple interest is:
$$ \text{SI} = \frac{P \times R \times T}{100} $$
Where:
- SI = Simple Interest = ₹8,000
- R = Rate of Interest = 10% per annum
- T = Time Period = 2 years
- P = Principal Amount (which we need to find)
To find the Principal (P), we can rearrange the formula:
$$ P = \frac{\text{SI} \times 100}{R \times T} $$
Now, substitute the given values:
$$ P = \frac{8000 \times 100}{10 \times 2} $$
$$ P = \frac{800000}{20} $$
$$ P = 40000 $$
So, the principal amount is ₹40,000.
Step 2: Calculating Compound Interest
Now that we have the Principal (P = ₹40,000), Rate (R = 10%), and Time (T = 2 years), we can calculate the compound interest compounded annually.
First, let's find the total amount (A) after 2 years using the compound interest formula:
$$ A = P \left(1 + \frac{R}{100}\right)^T $$
Substitute the values:
$$ A = 40000 \left(1 + \frac{10}{100}\right)^2 $$
$$ A = 40000 \left(1 + 0.1\right)^2 $$
$$ A = 40000 \left(1.1\right)^2 $$
$$ A = 40000 \times 1.21 $$
$$ A = 48400 $$
The total amount after 2 years is ₹48,400.
The compound interest (CI) is the difference between the total amount (A) and the principal (P):
$$ \text{CI} = A - P $$
$$ \text{CI} = 48400 - 40000 $$
$$ \text{CI} = 8400 $$
Therefore, the compound interest on the sum for the same period at the same rate compounded annually is ₹8,400.
Summary of Calculation
The key steps involved finding the principal amount from the simple interest details and then applying the compound interest formula. The difference between the calculated amount and the principal gives the compound interest.
| Component | Value |
|---|---|
| Simple Interest (SI) | ₹8,000 |
| Rate (R) | 10% p.a. |
| Time (T) | 2 years |
| Principal (P) | ₹40,000 |
| Compound Interest (CI) | ₹8,400 |
Similar Questions
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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:
