The simple interest on a sum is 7/8 of the principal for 5 years. What is the rate (in percentage) of interest per annum?

Options

A. 15
B. 17.5
C. 14
D. 22.5

Answer

To find the rate of interest per annum when the simple interest is given as \( \frac{7}{8} \) of the principal over a period of 5 years, we can follow these steps:

### Step 1: Understand the relationship between Simple Interest, Principal, Rate, and Time
The formula for Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Set up the equation based on the information given
From the problem, we know that:
\[ SI = \frac{7}{8} P \]
and the time \( T = 5 \) years.

### Step 3: Substitute the values into the SI formula
Substituting \( SI \) and \( T \) into the formula, we have:
\[ \frac{7}{8} P = \frac{P \times R \times 5}{100} \]

### Step 4: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{7}{8} = \frac{R \times 5}{100} \]

### Step 5: Cross-multiply to solve for \( R \)
Cross-multiplying gives:
\[ 7 \times 100 = 8 \times 5R \]
\[ 700 = 40R \]

### Step 6: Solve for \( R \)
Now, divide both sides by 40 to find \( R \):
\[ R = \frac{700}{40} = 17.5 \]

### Step 7: Conclusion
The rate of interest per annum is \( 17.5\% \).

### Final Answer
The correct answer is \( 17.5\% \) (Option B).

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