Rahul invests his savings, which is Rs. 25,000 in his bank that pays 7 per cent annual interest. How much will he earn by way of interest in one year?
Rs. 1,750
Calculating Annual Interest on Savings
This question asks us to determine the amount of interest earned on a principal investment of Rs. 25,000 over one year at an annual interest rate of 7 per cent. This is a classic problem involving the calculation of simple interest.
Understanding the Investment Problem
We are given the following information:
- Principal amount (the initial investment): Rs. 25,000
- Annual interest rate: 7 per cent per annum
- Time period: 1 year
We need to find the total interest earned over this one-year period.
Simple Interest Formula
Simple interest is calculated using a straightforward formula where the interest is only on the principal amount. The formula for simple interest (SI) is:
\( \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \)
Where:
- Principal (P) is the initial amount invested or borrowed.
- Rate (R) is the annual interest rate (in percentage).
- Time (T) is the time the money is invested or borrowed for (in years).
Step-by-Step Calculation of Interest
Let's plug the given values into the simple interest formula:
- Principal (P) = Rs. 25,000
- Rate (R) = 7%
- Time (T) = 1 year
Using the formula:
\( \text{SI} = \frac{25000 \times 7 \times 1}{100} \)
Now, let's perform the calculation:
\( \text{SI} = \frac{25000 \times 7}{100} \)
We can cancel out the two zeros in the numerator (from 25000) with the two zeros in the denominator (100):
\( \text{SI} = 250 \times 7 \)
Multiplying 250 by 7:
\( 250 \times 7 = 1750 \)
So, the simple interest earned in one year is Rs. 1,750.
Result: Interest Earned
Rahul will earn Rs. 1,750 by way of interest in one year on his investment of Rs. 25,000 at a 7 per cent annual interest rate.
| Component | Value |
|---|---|
| Principal (P) | Rs. 25,000 |
| Annual Rate (R) | 7% |
| Time (T) | 1 Year |
| Simple Interest (SI) | Rs. 1,750 |
Revision Table: Key Financial Concepts
| Term | Definition | Formula (for Simple Interest) |
|---|---|---|
| Principal | The initial amount of money invested or borrowed. | P |
| Interest Rate | The percentage charged or paid on the principal over a specific period (usually per year). | R (as a percentage, use R/100 in calculation) |
| Time | The duration for which the money is invested or borrowed. | T (in years) |
| Simple Interest | Interest calculated only on the principal amount. | \( \text{SI} = \frac{P \times R \times T}{100} \) |
| Amount | The total sum after adding interest to the principal (Principal + Interest). | \( \text{Amount} = P + \text{SI} \) |
Additional Information: Simple vs. Compound Interest
It's important to distinguish between simple interest and compound interest.
- Simple Interest: As calculated in this problem, simple interest is earned only on the original principal amount. The interest earned each period remains constant if the principal and rate are unchanged.
- Compound Interest: Compound interest is calculated on the principal amount AND the accumulated interest from previous periods. This means that interest earns interest, leading to faster growth of the investment over time compared to simple interest. Most bank savings accounts and investments today use compound interest. However, this specific problem is clearly about simple interest for one year, where simple and compound interest amounts are the same for the first period.
Understanding how interest is calculated is crucial for managing personal finances and making informed investment decisions.
Important Questions from Problem Solving
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