Question

A sum of money becomes ₹9600 in 2 years and ₹11520 in 3 years at compound interest. The rate of interest per annum is:

• A. 10%
• B. 15%
• C. 20%
• D. 25%

Hint:

Whenever you are given the compound interest amounts for two consecutive years, you can treat it like a simple interest problem for that single year gap! Just find the percentage increase from the first amount to the second: $\frac{\text{Increase}}{\text{Original Amount}} \times 100$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In compound interest, the total accumulated amount at the end of any given year automatically acts as the starting principal for the subsequent year. Therefore, the difference between the amount at the end of the 3rd year and the amount at the end of the 2nd year is purely the interest earned on the 2nd year's amount during that one-year interval.

Step 2: Key Formula or Approach:
1. $\text{Interest for the 3rd year} = \text{Amount after 3 years } (A_3) - \text{Amount after 2 years } (A_2)$ 2. $\text{Rate of Interest (R)} = \left( \frac{\text{Interest for the 3rd year}}{\text{Amount after 2 years } (A_2)} \right) \times 100$

Step 3: Detailed Explanation:
From the given data: Amount after 2 years ($A_2$) = ₹9600 Amount after 3 years ($A_3$) = ₹11520 Calculate the interest accumulated specifically during the third year: \[ \text{Interest for the 3rd year} = 11520 - 9600 = \text{₹}1920 \] Since this interest of ₹1920 was yielded entirely by the principal amount of ₹9600 over a single year, we can calculate the annual rate of interest ($R$) as follows: \[ R = \frac{1920}{9600} \times 100 \] \[ R = \frac{192}{960} \times 100 = \frac{1}{5} \times 100 = 20% \]

Step 4: Final Answer:
The rate of interest per annum is 20%.