At what rate will 14400 give 4032 as simple interest in 3 years and 6 months ?

Options

A. 8
B. 9
C. 8 1/2
D. none of these

Answer

To find the rate at which a principal amount of 14400 will yield a simple interest of 4032 in 3 years and 6 months, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = 14400
- Simple Interest (SI) = 4032
- Time (T) = 3 years and 6 months = 3.5 years = \( \frac{7}{2} \) years

### Step 2: Use the Simple Interest formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- SI = Simple Interest
- P = Principal
- R = Rate of interest per annum
- T = Time in years

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula gives:
\[ 4032 = \frac{14400 \times R \times \frac{7}{2}}{100} \]

### Step 4: Simplify the equation
To eliminate the fraction, we can multiply both sides by 100:
\[ 403200 = 14400 \times R \times \frac{7}{2} \]

### Step 5: Rearrange to solve for R
Now, isolate R:
\[ R = \frac{403200 \times 2}{14400 \times 7} \]

### Step 6: Calculate the values
Calculate the denominator:
\[ 14400 \times 7 = 100800 \]
Now plug this back into the equation for R:
\[ R = \frac{403200 \times 2}{100800} \]
\[ R = \frac{806400}{100800} \]
Now simplify:
\[ R = 8 \]

### Step 7: State the final answer
Thus, the rate of interest is:
\[ R = 8\% \]