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Amit borrowed Rs. 24000 at 10 percent per annum rate of compound interest. He repaid a certain amount at the end of the first year. Then he paid Rs. 20240 at the end of the secondyear to completely discharge the loan. What amount did he repay at the end of the first year?

Amit borrowed Rs. 24000 at 10 percent per annum rate of compound interest. He repaid a certain amount at the end of the first year. Then he paid Rs. 20240 at the end of the secondyear to completely discharge the loan. What amount did he repay at the end of the first year? Correct Answer Rs. 8000

Rs. 24000 at 10% per annum at the end of first year = 24000 × (1 + 0.1) = Rs. (24000 × 1.1) = Rs. 26400

Let ‘a’ be the amount repaid at the end of the first year

Balance amount to be repaid = (26400 - a)

Again at 10% per annum, this amount will become (26400 - a) × 1.1 = (29040 - 1.1a)

Given this is equal to Rs. 20240

⇒ 29040 - 1.1a = 20240

⇒ 1.1a = 29040 - 20240

⇒ 1.1a = 8800

⇒ a = (8800/1.1)

⇒ a = Rs. 8000

∴ Amount which he repaid at the end of the first year = Rs. 8000

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