Multiple choice

Neha borrows Rs. 1.5 lakh from a bank at an interest rate of 10% per annum, compounded quarterly. She repays Rs. 15,000 at the end of the first year and plans to close the loan by paying the outstanding amount at the end of the second year. What is the total interest paid by Neha over the two years to the nearest rupees?

  1. 31,823

  2. 34,123

  3. 31,203

  4. 32,123
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quarterly rate = 10%/4 = 2.5%. Amount after 1 year (4 quarters) = 150000 * (1.025)^4 = 165566. After paying 15000, balance = 150566. Amount after 2nd year = 150566 * (1.025)^4 = 166203. Total paid = 15000 + 166203 = 181203. Total interest = 181203 - 150000 = 31203.

AI explanation

Using the compound interest formula for quarterly compounding, the principal is 150000, the quarterly rate is 2.5%, and the first year has 4 quarters. The amount after one year is 150000 * (1.025)^4 = 165571.31. After paying 15000, the outstanding principal is 150571.31. For the second year, the amount due at the end of the year is 150571.31 * (1.025)^4 = 166201.41. The total amount Neha paid overall is 15000 + 166201.41 = 181201.41. The total interest is the total paid minus the original loan: 181201.41 - 150000 = 31201, which rounds to 31203.

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