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 are dealing with a Simple Interest (SI) scenario where the final amount (Principal + Interest) becomes twice the initial Principal after 8 years. We need to find the annual interest rate \(R\).
Step 2: Key Formula or Approach:

Simple Interest Formula: \(SI = \frac{P \times R \times T}{100}\)

Amount \(A = P + SI\)

If money doubles, \(A = 2P\), which implies \(SI = A - P = 2P - P = P\).

Step 3: Detailed Explanation:

Setup: Let the Principal amount be \(P\). Since the money doubles itself, the final amount \(A\) is \(2P\).

Calculating Interest: The Interest earned over the period is \(SI = 2P - P = P\).

Using the SI Formula:
Substitute the values into \(SI = \frac{P \times R \times T}{100}\):
\[P = \frac{P \times R \times 8}{100}\]

Solving for R:
The \(P\) on both sides cancels out (since \(P \neq 0\)).
\[1 = \frac{R \times 8}{100}\]
\[R = \frac{100}{8}\]

Final Division:
\[R = 12.5%\]

Interpretation: This means the principal grows by \(12.5%\) of its original value every year. In 8 years, it grows by \(12.5 \times 8 = 100%\), effectively doubling the original amount.

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