Understanding the Interest Calculation Problem
This problem asks us to find the difference between two types of interest calculations: compound interest and simple interest. We are given the principal amount, time period, and interest rates for both scenarios.
- Principal Amount (\(P\)): ₹ 1000
- Time Period (\(T\)): 3 years
Calculating Compound Interest (\(x\))
First, let's calculate the compound interest (\(x\)) on ₹ 1000 at a rate of 10% per annum, compounded annually for 3 years.
The formula for the final amount (\(A\)) with compound interest is:
\( A = P \left(1 + \frac{R}{100}\right)^T \)
Where:
- \(P\) = Principal Amount = ₹ 1000
- \(R\) = Annual Interest Rate = 10%
- \(T\) = Time Period in years = 3
Substituting the values:
\( A = 1000 \left(1 + \frac{10}{100}\right)^3 \)
\( A = 1000 \left(1 + 0.1\right)^3 \)
\( A = 1000 \left(1.1\right)^3 \)
\( A = 1000 \times 1.331 \)
\( A = 1331 \)
The total amount after 3 years is ₹ 1331.
Now, we find the compound interest (\(x\)) by subtracting the principal from the final amount:
\( x = \text{Amount} - \text{Principal} \)
\( x = 1331 - 1000 \)
\( x = 331 \)
So, the compound interest (\(x\)) is ₹ 331.
Calculating Simple Interest (\(y\))
Next, let's calculate the simple interest (\(y\)) on ₹ 1000 at an annual rate of 11% for 3 years.
The formula for simple interest (\(SI\)) is:
\( SI = \frac{P \times R \times T}{100} \)
Where:
- \(P\) = Principal Amount = ₹ 1000
- \(R\) = Annual Interest Rate = 11%
- \(T\) = Time Period in years = 3
Substituting the values:
\( y = \frac{1000 \times 11 \times 3}{100} \)
\( y = 10 \times 11 \times 3 \)
\( y = 330 \)
So, the simple interest (\(y\)) is ₹ 330.
Finding the Difference Between Interests
The question asks for the difference between the compound interest (\(x\)) and the simple interest (\(y\)).
Difference = \(x - y\)
Difference = ₹ 331 - ₹ 330
Difference = ₹ 1
Summary Table
| Interest Type | Principal (₹) | Rate (%) | Time (Years) | Calculated Interest (₹) |
|---|---|---|---|---|
| Compound Interest (\(x\)) | 1000 | 10% (Annual) | 3 | 331 |
| Simple Interest (\(y\)) | 1000 | 11% (Annual) | 3 | 330 |
The difference between the calculated compound interest and simple interest is ₹ 1.
Similar Questions
- If the rate of interest is 5%, then what would be the difference between compound interest and simple interest received on ₹10,000 (each) after 3 years from now?
Important Questions from Simple and Compound Both
X took a loan of Rs.1400 with simple interest for as many years as the rate of interest. If he paid Rs.1210 as interest at the end of that period, what was the rate of interest?
The S.I. on a certain sum of money for 4 years at 4 percent per annum exceeds the C.I. on the same sum for 3 years at 5 percent per annum by Rs. 57. Find the approximate sum.
Compound interest on a certain sum of money for 2 years at a rate of 'r' per cent per annum (compounding annually) is Rs. 8385. Simple interest on the same sum at the same rate for 2 years is Rs 7800. What is the value of r?
Find the difference between compound interest and simple interest on a sum of Rs. 5000 at 10% per annum for 3 years.
The difference between the compound interest and simple interest on a certain sum of money in 3 years at 5% p.a. is Rs. 6,100. What is the initial amount?
