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

### Concept & Present Value of Instalments The sum borrowed (Principal) is the total present value of all future instalments discounted at the given interest rate. $$P = \frac{x}{\left(1 + \frac{R}{100}\right)} + \frac{x}{\left(1 + \frac{R}{100}\right)^2}$$ ### Step-by-Step Solution * **Given:** Instalment $x = 882$, Rate $R = 5\%$. * The fractional rate is $1 + \frac{5}{100} = 1 + \frac{1}{20} = \frac{21}{20}$. * $P = \frac{882}{\frac{21}{20}} + \frac{882}{\left(\frac{21}{20}\right)^2}$ * $P = 882 \times \frac{20}{21} + 882 \times \frac{400}{441}$ * Calculate the first term: $882 \div 21 = 42$, so $42 \times 20 = 840$. * Calculate the second term: $882 \div 441 = 2$, so $2 \times 400 = 800$. * Sum the present values: $P = 840 + 800 = 1640$. ### Exam Strategy & Shortcut Recognize that $882$ is exactly $2 \times 441$, which is a strong hint since $21^2 = 441$. This makes the cancellation immediate: $2 \times 21 \times 20 + 2 \times 400 = 840 + 800 = 1640$. ### Common Pitfall Students sometimes incorrectly multiply the instalment amount by the number of years and then subtract interest, effectively confusing simple interest arithmetic with compound discounting. ### Final Answer Therefore, the correct answer is **₹ 1640**.