Question

A sum of Rs. 10,000 is invested at 5% per annum compound interest for 2 years. What is the total amount?

• A. Rs. 11,000
• B. Rs. 11,025
• C. Rs. 11,050
• D. Rs. 11,100

Hint:

Compute compound interest using \( A = P (1 + \frac{r}{100})^n \) and verify with binomial expansion for small rates.

Answer 1

The Correct Option is B

We need the total amount after 2 years of compound interest.
- Step 1: Recall compound interest formul(a) Amount \( A = P \left(1 + \frac{r}{100}\right)^n \), where \( P \) is principal, \( r \) is rate, \( n \) is time.
- Step 2: Assign values. \( P = 10000 \), \( r = 5 \), \( n = 2 \).
\[ A = 10000 \left(1 + \frac{5}{100}\right)^2 = 10000 \times (1.05)^2 \] - Step 3: Calculate \( (1.05)^2 \).
\[ 1.05 \times 1.05 = 1.1025 \] - Step 4: Compute amount.
\[ A = 10000 \times 1.1025 = 11025 \] - Step 5: Alternative metho(d) Use binomial expansion for precision:
\[ (1.05)^2 = 1 + 2 \times 0.05 + (0.05)^2 = 1 + 0.1 + 0.0025 = 1.1025 \] \[ A = 10000 \times 1.1025 = 11025 \] - Step 6: Check options.
- (a) 11,000: Incorrect.
- (b) 11,025: Correct.
- (c) 11,050: Incorrect.
- (d) 11,100: Incorrect.
- Step 7: Verify. Simple interest check (for contrast): \( SI = 10000 \times 5% \times 2 = 1000 \), total = 11000, which is less than compound interest, confirming calculation.
Thus, the answer is b.