At 12% simple interest per annum a sum of money becomes Rs. 295 in \(1\frac{1}{2}\) years. What was the sum invested?
Rs. 250
Calculating the Original Sum Invested using Simple Interest
This question asks us to find the initial sum of money, also known as the Principal, that was invested. We are given the final amount, the simple interest rate, and the time period. We will use the formulas for simple interest and amount to solve this problem.
Let's identify the given information:
- Amount (\(A\)) = Rs. 295
- Simple Interest Rate (\(R\)) = 12% per annum
- Time (\(T\)) = \(1\frac{1}{2}\) years
We need to find the Principal (\(P\)).
First, let's convert the time from a mixed fraction to a simple fraction or decimal:
\(T = 1\frac{1}{2} \text{ years} = 1 + \frac{1}{2} \text{ years} = \frac{2}{2} + \frac{1}{2} \text{ years} = \frac{3}{2} \text{ years} = 1.5 \text{ years}\)
The formula for Simple Interest (\(SI\)) is:
\(SI = \frac{P \times R \times T}{100}\)
The Amount (\(A\)) received at the end of the time period is the sum of the Principal (\(P\)) and the Simple Interest (\(SI\)):
\(A = P + SI\)
We can substitute the formula for \(SI\) into the formula for \(A\):
\(A = P + \frac{P \times R \times T}{100}\)
We can factor out \(P\) from the right side of the equation:
\(A = P \left(1 + \frac{R \times T}{100}\right)\)
Now, we can plug in the given values into this formula:
\(295 = P \left(1 + \frac{12 \times 1.5}{100}\right)\)
Let's simplify the term inside the parentheses:
\(1 + \frac{12 \times 1.5}{100} = 1 + \frac{18}{100} = 1 + 0.18 = 1.18\)
So the equation becomes:
\(295 = P \times 1.18\)
To find \(P\), we need to divide the Amount by \(1.18\):
\(P = \frac{295}{1.18}\)
Let's perform the division:
\(P = 250\)
So, the sum invested (Principal) was Rs. 250.
Summary of the Calculation
| Given | Value |
|---|---|
| Amount (A) | Rs. 295 |
| Rate (R) | 12% per annum |
| Time (T) | \(1\frac{1}{2}\) years or 1.5 years |
| Formula Used | Explanation |
|---|---|
| \(A = P \left(1 + \frac{R \times T}{100}\right)\) | Amount equals Principal plus Simple Interest |
Substituting values and solving for P:
\(295 = P \left(1 + \frac{12 \times 1.5}{100}\right)\)
\(295 = P \left(1 + \frac{18}{100}\right)\)
\(295 = P (1 + 0.18)\)
\(295 = P \times 1.18\)
\(P = \frac{295}{1.18}\)
\(P = 250\)
The sum invested was Rs. 250.
Revision Table: Key Simple Interest Concepts
| Term | Definition | Formula |
|---|---|---|
| Principal (P) | The initial sum of money invested or borrowed. | - |
| Rate (R) | The percentage of the principal charged as interest per period (usually per year). | - |
| Time (T) | The duration for which the money is invested or borrowed. | - |
| Simple Interest (SI) | Interest calculated only on the initial principal amount. | \(SI = \frac{P \times R \times T}{100}\) |
| Amount (A) | The total sum of money at the end of the period, including principal and interest. | \(A = P + SI\) or \(A = P \left(1 + \frac{R \times T}{100}\right)\) |
Additional Information on Simple Interest Calculations
Simple interest is a basic concept in finance. It is calculated on the original principal only, regardless of the interest earned in previous periods. This is different from compound interest, where interest is calculated on the principal amount and also on the accumulated interest from previous periods.
Understanding how to calculate the principal amount when the final amount, rate, and time are given is a common type of problem. The key is to use the relationship between Amount, Principal, and Simple Interest. By rearranging the formulas, you can find any missing value if the others are known.
Always make sure the time period and the interest rate match. For example, if the rate is per annum, the time should be in years. If time is given in months, convert it to years by dividing by 12. If time is given in days, convert it to years by dividing by 365 (or 366 for a leap year, although often 365 is used unless specified).
In this problem, the time was given as \(1\frac{1}{2}\) years, which is already in years, making the calculation straightforward after converting the mixed fraction.
Similar Questions
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?
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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?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
