What sum of money must be given as simple interset for six months at 4 % per annum in order to earn Rs 150 interest ?

Options

A. Rs 5000
B. Rs 7500
C. Rs 10000
D. Rs 15000

Answer

To solve the problem of finding the sum of money that must be given as simple interest for six months at 4% per annum in order to earn Rs 150 interest, we can follow these steps:

### Step 1: Understand the Simple Interest Formula
The formula for calculating simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) is the simple interest,
- \( P \) is the principal amount (the sum of money we need to find),
- \( R \) is the rate of interest per annum,
- \( T \) is the time in years.

### Step 2: Convert Time into Years
The time given in the question is 6 months. Since the formula requires time in years:
\[ T = \frac{6}{12} = 0.5 \text{ years} \]

### Step 3: Substitute Known Values into the Formula
We know:
- \( SI = 150 \) (the interest earned),
- \( R = 4\% \),
- \( T = 0.5 \) years.

Substituting these values into the formula:
\[ 150 = \frac{P \times 4 \times 0.5}{100} \]

### Step 4: Simplify the Equation
Now simplify the equation:
\[ 150 = \frac{P \times 2}{100} \]
Multiplying both sides by 100 to eliminate the fraction:
\[ 15000 = P \times 2 \]

### Step 5: Solve for Principal (P)
Now, divide both sides by 2 to isolate \( P \):
\[ P = \frac{15000}{2} = 7500 \]

### Conclusion
The sum of money that must be given as simple interest for six months at 4% per annum to earn Rs 150 interest is **Rs 7500**.

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