Question

Find the compound interest on ₹8000 for 2 years at 10% per annum compounded annually.

• A. ₹1680
• B. ₹1720
• C. ₹1760
• D. ₹1800

Hint:

For 2 years at a 10% rate, you can shortcut the formula with net effective percentage growth! The effective rate is: $$10 + 10 + \frac{10 \times 10}{100} = 21\%$$ Simply calculate $21\%$ of $8000$: $80 \times 21 = \text{₹}1680$ in one single step!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Compound interest means you earn interest on top of interest. Every year, the interest generated is added back into the principal amount, forming a brand new base balance for the subsequent year.

Step 2: Key Formula or Approach:
1. Total Amount formula: $A = P\left(1 + \frac{R}{100}\right)^n$ 2. Compound Interest formula: $CI = A - P$ Where: $P = \text{Principal amount} = \text{₹}8000$ $R = \text{Rate of interest per annum} = 10\%$ $n = \text{Number of years} = 2$

Step 3: Detailed Explanation:
Substitute our values directly into the total accumulation formula: \[ A = 8000 \times \left(1 + \frac{10}{100}\right)^2 \] \[ A = 8000 \times \left(\frac{11}{10}\right)^2 \] \[ A = 8000 \times \frac{121}{100} \] Cancel out the zeros to simplify multiplication: \[ A = 80 \times 121 = \text{₹}9680 \] Now, isolate the specific compound interest component by subtracting the initial principal base: \[ CI = A - P \] \[ CI = 9680 - 8000 = \text{₹}1680 \]

Step 4: Final Answer:
The total compound interest amount is ₹1680.