Question

A sum of money becomes 7 times itself in 2 years at a certain rate of simple interest. Find the rate of interest per annum.

• A. 100%
• B. 10%
• C. 200%
• D. 300%

Hint:

For these problems, you can use the direct formula: $R = \frac{(n-1) \times 100}{T}$. Here, $R = \frac{(7-1) \times 100}{2} = \frac{600}{2} = 300\%$.

Answer 1

The Correct Option is D

Step 1 : Understanding the Question
This problem deals with Simple Interest (SI), where interest is earned only on the initial principal amount. The phrase "becomes 7 times itself" refers to the 'Amount,' which includes both the original principal and the interest earned over two years. The objective is to work backward from the final amount to find the annual rate of interest.
Step 2 : Key Formulas and approach
The strategy is to define the Principal as a variable (usually 'x' or '100') and then determine the Interest by subtracting the Principal from the final Amount. Once the Interest is known, we use the standard Simple Interest formula to find the missing Rate (R).
Key Formulas:
1. $\text{Interest (I)} = \text{Amount (A)} - \text{Principal (P)}$
2. $I = \frac{P \times R \times T}{100}$
Step 3 : Detailed Explanation

Defining Variables: Let the Principal ($P$) be Rs. 100. Since the sum becomes 7 times itself, the final Amount ($A$) is $100 \times 7 = Rs. 700$.

Calculating Total Interest: The total simple interest earned over the period is $A - P$, which is $700 - 100 = Rs. 600$.

Setting up the SI Formula: We plug the values into the formula: $600 = \frac{100 \times R \times 2}{100}$. Here, $T = 2$ years.

Solving for R: The '100' in the numerator and denominator cancel out, leaving us with $600 = 2R$. Dividing both sides by 2 gives $R = 300$.

Verification: If the rate is 300%, the interest for 1 year on 100 is 300. For 2 years, it is 600. Total amount = $100 + 600 = 700$, which is 7 times the principal. The logic is correct.


Step 4 : Final Answer
The annual rate of simple interest is 300%, which is option (D).