Question

A sum of money at simple interest doubles itself in 8 years. What is the rate of interest per annum?

• A. 10.50%
• B. 12%
• C. 12.50%
• D. 15%
• E. 20%

Hint:

If a sum becomes 'n' times itself in 'T' years at simple interest, you can use the direct shortcut formula: \(R = \frac{(n - 1) \times 100}{T}\). For doubling, \(n=2\), so \(R = \frac{100}{T}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to find the annual rate of simple interest at which an initial principal amount becomes twice its value over a period of 8 years.


Step 2: Key Formula or Approach:
The formula for Simple Interest is: \[ SI = \frac{P \times R \times T}{100} \] When a sum doubles, the Amount (\(A\)) becomes \(2P\), which implies the accumulated interest is equal to the principal (\(SI = P\)).


Step 3: Detailed Explanation:
Let the principal sum be \(P\). Given that the sum doubles itself, the Amount (\(A\)) = \(2P\). The Simple Interest (\(SI\)) earned is: \[ SI = A - P = 2P - P = P \] The given time period (\(T\)) is 8 years. Substitute these values into the Simple Interest formula: \[ P = \frac{P \times R \times 8}{100} \] Cancel \(P\) from both sides: \[ 1 = \frac{8R}{100} \] Rearrange to solve for the rate (\(R\)): \[ 8R = 100 \] \[ R = \frac{100}{8} \] \[ R = 12.5\% \]

Step 4: Final Answer:
The rate of interest per annum is 12.50%.