The simple interest on a sum for 20 years is 5/4 of the principal. What is the per annum rate (in percentage) of interest?

Options

A. 6.25
B. 12.5
C. 2.5
D. 5

Explanation

To solve the problem step by step, we need to find the per annum rate of interest given that the simple interest (SI) for 20 years is \( \frac{5}{4} \) of the principal (P).

### Step 1: Understand the formula for Simple Interest
The formula for Simple Interest 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
From the problem, we know that:
\[ SI = \frac{5}{4} P \]
And the time \( T = 20 \) years. Substituting these values into the formula gives:
\[ \frac{5}{4} P = \frac{P \times R \times 20}{100} \]

### Step 3: Simplify the equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{5}{4} = \frac{R \times 20}{100} \]

### Step 4: Solve for R
To isolate \( R \), we can multiply both sides by 100:
\[ 100 \times \frac{5}{4} = R \times 20 \]
This simplifies to:
\[ 125 = R \times 20 \]

Now, divide both sides by 20 to find \( R \):
\[ R = \frac{125}{20} = 6.25 \]

### Step 5: Convert R to percentage
Since \( R \) is already in percentage form, we conclude that:
\[ R = 6.25\% \]

### Final Answer
The per annum rate of interest is \( 6.25\% \).

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