At 9.5% simple interest per annum, a sum of money became Rs. 942 in 6 years. The sum invested initially was:
Rs. 600
Understanding Simple Interest Calculations
This problem asks us to find the initial sum of money, also known as the principal, that was invested. We are given the simple interest rate per annum, the time period for which the money was invested, and the final amount received after the interest was added to the principal.
Given Information:
- Amount (A) = Rs. 942
- Rate of Simple Interest (R) = 9.5% per annum
- Time Period (T) = 6 years
We need to find the Principal (P).
Simple Interest Formula
The formula for calculating simple interest is:
\( \text{Simple Interest (SI)} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \)
Where:
- \( \text{P} \) is the Principal amount
- \( \text{R} \) is the Rate of interest per annum
- \( \text{T} \) is the Time period in years
The Amount (A) received at the end of the time period is the sum of the Principal and the Simple Interest:
\( \text{A} = \text{P} + \text{SI} \)
Calculating the Principal Amount
We can substitute the formula for Simple Interest (SI) into the Amount formula:
\( \text{A} = \text{P} + \frac{\text{P} \times \text{R} \times \text{T}}{100} \)
Now, we can factor out P from the right side:
\( \text{A} = \text{P} \left( 1 + \frac{\text{R} \times \text{T}}{100} \right) \)
To find the Principal (P), we can rearrange the formula:
\( \text{P} = \frac{\text{A}}{1 + \frac{\text{R} \times \text{T}}{100}} \)
Step-by-Step Calculation
Let's plug in the given values into the derived formula for P:
\( \text{P} = \frac{942}{1 + \frac{9.5 \times 6}{100}} \)
First, calculate the product of Rate and Time:
\( 9.5 \times 6 = 57 \)
Now, substitute this back into the formula:
\( \text{P} = \frac{942}{1 + \frac{57}{100}} \)
Convert the fraction to a decimal:
\( \frac{57}{100} = 0.57 \)
Add this to 1 in the denominator:
\( 1 + 0.57 = 1.57 \)
Finally, perform the division to find P:
\( \text{P} = \frac{942}{1.57} \)
\( \text{P} = 600 \)
So, the sum invested initially was Rs. 600.
Conclusion
The principal amount invested at 9.5% simple interest per annum that grew to Rs. 942 in 6 years is Rs. 600.
Revision Table: Simple Interest Components
| Component | Description | Symbol Used |
|---|---|---|
| Principal | The initial amount of money invested or borrowed. | P |
| Rate | The percentage at which interest is charged or earned per time period (usually per year). | R |
| Time | The duration for which the money is invested or borrowed. | T |
| Simple Interest | The interest calculated only on the principal amount. | SI |
| Amount | The total sum including the principal and the accrued interest at the end of the time period. | A |
Additional Information on Simple Interest
Simple interest is a basic and quick method of calculating the interest charge on a loan or investment. It is calculated only on the principal amount, and the interest earned is not added back to the principal to earn further interest. This is unlike compound interest, where interest is added to the principal, and subsequent interest is calculated on the new, larger principal.
Key points about simple interest:
- Interest is fixed for the entire duration based on the initial principal.
- It is commonly used for short-term loans or simple financial transactions.
- The total interest earned over time is directly proportional to the principal, rate, and time.
Understanding simple interest is fundamental to grasping more complex financial concepts.
Similar Questions
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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?
