Multiple choice

Sunita borrows Rs. 4 lakhs at an interest rate of 10% per annum, compounded half-yearly. She repays Rs. 24,200 at the end of the first year and settles the remaining loan at the end of the third year. The total interest, in rupees, paid over the three years is nearest to:

  1. 1,03,200

  2. 1,03,280

  3. 1,30,823

  4. 1,13,820
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = 400,000. Rate = 10% p.a. compounded half-yearly (5% every 6 months). Year 1: 400,000 * (1.05)^2 = 441,000. Repay 24,200, balance = 416,800. Year 2: 416,800 * (1.05)^2 = 459,558. Year 3: 459,558 * (1.05)^2 = 506,658. Total interest = 506,658 + 24,200 - 400,000 = 130,858. Nearest option is 1,30,823.

AI explanation

Using the compound interest formula for half-yearly compounding, the loan amount at the end of the first year is 400000 times 1.05 squared, which equals 441000. After the repayment of 24200, the outstanding principal becomes 416800. This amount compounds for two more years, so the amount due at the end of the third year is 416800 times 1.05 to the power of 4, which equals 506823. The total amount paid is 24200 plus 506823 equals 531023, making the total interest paid 531023 minus 400000 equals 131023. Since 131023 is closest to 130823, the total interest paid is nearest to 1,30,823.

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