Question

A sum of money is borrowed and paid back in two annual instalments of Rs.\ 882 each, allowing 5% compound interest. The sum borrowed was

• A. Rs.\ 1600
• B. Rs.\ 1620
• C. Rs.\ 1640
• D. Rs.\ 1680
• E. Rs.\ 1650

Answer 1

The Correct Option is C

Concept: Present value of instalments: \[ \text{Principal} = \frac{A}{(1+r)} + \frac{A}{(1+r)^2} \]
Step 1: Substitute values.
\[ A = 882,\quad r = 5% = 0.05 \] \[ P = \frac{882}{1.05} + \frac{882}{(1.05)^2} \]
Step 2: Calculate.
\[ \frac{882}{1.05} = 840 \] \[ \frac{882}{1.1025} = 800 \] \[ P = 840 + 800 = 1640 \]
Step 3: Option analysis.

• (A) Incorrect $\times$
• (B) Incorrect $\times$
• (C) Correct \checkmark
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (C).