The interest earned on Rs. 1,600 at the rate of 5% simple interest per annum for 6 years would be:
Rs. 480
This question asks us to calculate the simple interest earned on a specific principal amount over a certain period at a given annual interest rate. Understanding how simple interest works is fundamental in finance.
Understanding Simple Interest Calculation
Simple interest is calculated only on the principal amount. It does not compound, meaning the interest earned in previous periods is not added to the principal for calculating interest in the current period.
The formula for simple interest is:
\( \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} \)
Where:
- Principal (P): The initial amount of money borrowed or invested.
- Rate (R): The annual interest rate (expressed as a percentage).
- Time (T): The duration for which the money is borrowed or invested (in years).
Applying the Simple Interest Formula
In this problem, we are given the following information:
- Principal amount (P) = Rs. 1,600
- Rate of interest (R) = 5% per annum
- Time period (T) = 6 years
We need to find the Simple Interest (SI) earned.
Step-by-Step Simple Interest Calculation
Let's substitute the given values into the simple interest formula:
\( \text{SI} = \frac{1600 \times 5 \times 6}{100} \)
Now, let's perform the calculation:
First, multiply the numbers in the numerator:
\( 1600 \times 5 = 8000 \)
\( 8000 \times 6 = 48000 \)
So the formula becomes:
\( \text{SI} = \frac{48000}{100} \)
Now, divide by 100:
\( \text{SI} = 480 \)
Therefore, the simple interest earned is Rs. 480.
Comparing with Options
Let's look at the provided options:
- Option 1: Rs. 469
- Option 2: Rs. 2,080
- Option 3: Rs. 480
- Option 4: Rs. 450
Our calculated simple interest is Rs. 480, which matches Option 3.
Summary of Simple Interest Problem
To find the simple interest, we identified the principal, rate, and time and applied the standard formula \( SI = (P \times R \times T) / 100 \). The calculation led us to the result of Rs. 480 as the interest earned over 6 years.
Revision Table: Simple Interest Concepts
| Term | Definition | Unit |
|---|---|---|
| Principal (P) | Initial amount invested or borrowed | Currency (e.g., Rs.) |
| Rate (R) | Annual interest rate | Percentage (%) |
| Time (T) | Duration of investment/loan | Years |
| Simple Interest (SI) | Interest calculated only on the principal | Currency (e.g., Rs.) |
Additional Information on Interest Calculations
While simple interest is straightforward, another common type is compound interest. Compound interest is calculated on the principal amount and also on the accumulated interest from previous periods. This means that the principal amount grows over time, and the interest earned subsequently also grows, leading to faster growth of the investment or debt compared to simple interest.
Key differences include:
- Simple Interest: Interest is constant every year (based on the original principal).
- Compound Interest: Interest increases each year (based on principal + accumulated interest).
Understanding the distinction between simple and compound interest is crucial for personal finance, investments, and loans.
Similar Questions
At 5% simple interest per annum a certain sum yields a total amount of ₹2,790 at the end of 3\(\frac{1}{4}\) years. The sum invested was:
Saathi deposited Rs. 825 in a bank that promised 8% simple interest per annum. If Saathi kept the money with the bank for 5 years, she will earn an interest of:
- ₹ x invested at 9% simple interest per annum for 5 years yields the same interest as that on ₹ y invested at 7.5% simple interest per annum for 4 years. Find x ∶ y.
A sum of money invested for 2 years and 9 months at the rate of 8% simple interest per annum became Rs. 732 at the end of the period. What was the sum that was initially invested?
The simple interest on a certain sum for 3 years at 8% p.a is Rs. 90 more than simple interest at 9% p.a for 2 years on the same sum. The sum is (in rupees):
The interest earned on Rs. 3,675 at the rate of 4% simple interest per annum for 2 years will be?
A sum of money was invested at the rate of 7.5% simple interest per annuum for 4 years. If the investments were for 5 years, the interest earned would have been Rs. 375 more. What was the initial sum invested?
Rs. 750 invested for 3 months gave an interest of Rs. 18. What was the simple rate of interest per annum?
At 9.5% simple interest per annum, a sum of money became Rs. 942 in 6 years. The sum invested initially was:
At 12% simple interest per annum a sum of money becomes Rs. 295 in \(1\frac{1}{2}\) years. What was the sum invested?
Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
P borrowed an amount from Q at a simple interest of 10% p.a. At the end of the year, P paid back Rs 99000 which was 90% of what she owed. How much money did P borrow?
