Multiple choice

A sum of money is borrowed and paid back in two annual equal instalments of Rs 8820, allowing 5% per annum compound interest. Find the sum borrowed? एक व्यक्ति ने कुछ राशि उधार ली और उसे 8820रू. प्रतिवर्ष की दो समान किस्तों में लौटाया। यदि चक्रवृद्धि ब्याज 5 प्रतिशत वार्षिक दर से लिया जाता हो, तो उधार ली गई कुल राशि ज्ञात कीजिए?

  1. 17640

  2. 16980

  3. 16400

  4. 16200

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C Correct answer
Explanation

Let P be the sum borrowed. After 1st year: P × 1.05 - 8820 = remaining principal. After 2nd year: (P × 1.05 - 8820) × 1.05 = 8820 (final payment). Solving: P × 1.1025 - 8820 × 1.05 = 8820, so P × 1.1025 = 8820 + 9261 = 18081, giving P = 18081 / 1.1025 = 16400. Each installment includes both principal and compound interest.