At what rate percent per annum will a sum of money double in 6 year ?

Options

A. 16 2/3%
B. 18%
C. 17%
D. 19 2/3%

Answer

To find the rate percent per annum at which a sum of money will double in 6 years, we can follow these steps:

### Step 1: Understand the Problem
We need to determine the rate of interest (R) that will allow a principal amount (P) to double in 6 years. When the money doubles, the simple interest earned will be equal to the principal amount.

### Step 2: Set Up the Equation
Let the principal amount be P. If the money doubles in 6 years, the total amount (A) after 6 years will be:
\[ A = P + \text{Simple Interest} = P + P = 2P \]
The simple interest (SI) can be calculated using the formula:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- SI is the simple interest
- P is the principal amount
- R is the rate of interest per annum
- T is the time in years

### Step 3: Substitute Values
Since the simple interest earned is equal to the principal (P) when the amount doubles:
\[ P = \frac{P \times R \times 6}{100} \]

### Step 4: Cancel Out P
We can cancel P from both sides of the equation (assuming P is not zero):
\[ 1 = \frac{R \times 6}{100} \]

### Step 5: Solve for R
To isolate R, we multiply both sides by 100:
\[ 100 = R \times 6 \]
Now, divide both sides by 6:
\[ R = \frac{100}{6} \]
\[ R = \frac{50}{3} \]

### Step 6: Convert to Percentage
Now, we can convert \(\frac{50}{3}\) into a percentage:
\[ R = 16 \frac{2}{3} \% \]

### Conclusion
Thus, the rate percent per annum at which a sum of money will double in 6 years is:
\[ \boxed{16 \frac{2}{3} \%} \]

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