At what rate of simple interest per annum will a sum become 7/4 of itself in 4 years?

Options

A. `18%`
B. `20%`
C. `18(3)/(4)%`
D. `18(1)/(2)%`

Answer

To solve the problem of finding the rate of simple interest per annum at which a sum becomes \( \frac{7}{4} \) of itself in 4 years, we can follow these steps:

### Step 1: Define the Principal and Amount
Let the principal amount (P) be Rs. 4. According to the question, the amount (A) after 4 years will be \( \frac{7}{4} \) of the principal.

\[ A = \frac{7}{4} \times P = \frac{7}{4} \times 4 = 7 \]

### Step 2: Calculate the Interest Earned
The interest (I) earned over 4 years can be calculated as:

\[ I = A - P = 7 - 4 = 3 \]

### Step 3: Determine the Time Period
The time period (T) is given as 4 years.

### Step 4: Calculate the Simple Interest Rate
The formula for simple interest is:

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

Where:
- \( I \) is the interest earned,
- \( P \) is the principal amount,
- \( R \) is the rate of interest per annum,
- \( T \) is the time in years.

Rearranging the formula to find the rate \( R \):

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

Substituting the known values:

\[ R = \frac{3 \times 100}{4 \times 4} = \frac{300}{16} = 18.75 \]

### Step 5: Conclusion
The rate of simple interest per annum is \( 18.75\% \).

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