In how much time (in yeas) will Rs. 7200 amount to Rs. 8928 at simple interset at the rate of 8 % per annum ?

Options

A. 3
B. 4
C. 2
D. 6

Answer

To find out how much time it will take for Rs. 7200 to amount to Rs. 8928 at a simple interest rate of 8% per annum, we can follow these steps:

### Step 1: Calculate the Simple Interest
First, we need to determine the simple interest earned. The formula for simple interest (SI) is:

\[ SI = A - P \]

Where:
- \( A \) is the amount after time \( t \)
- \( P \) is the principal amount

Given:
- \( A = 8928 \)
- \( P = 7200 \)

Now, substituting the values:

\[ SI = 8928 - 7200 = 1728 \]

### Step 2: Use the Simple Interest Formula
The formula for simple interest is also given by:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) is the simple interest
- \( P \) is the principal amount
- \( R \) is the rate of interest per annum
- \( T \) is the time in years

We already have \( SI = 1728 \), \( P = 7200 \), and \( R = 8\% \). We need to find \( T \).

### Step 3: Rearranging the Formula to Solve for Time
Rearranging the simple interest formula to solve for \( T \):

\[ T = \frac{SI \times 100}{P \times R} \]

### Step 4: Substitute the Known Values
Now, substituting the known values into the formula:

\[ T = \frac{1728 \times 100}{7200 \times 8} \]

### Step 5: Calculate the Denominator
First, calculate the denominator:

\[ 7200 \times 8 = 57600 \]

### Step 6: Calculate Time
Now, substituting back into the equation:

\[ T = \frac{172800}{57600} \]

Now, performing the division:

\[ T = 3 \]

### Conclusion
Therefore, the time required for Rs. 7200 to amount to Rs. 8928 at a simple interest rate of 8% per annum is **3 years**.

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