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Compound interest with partial repayment

CAT 2023 Slot 2 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 Slot 2 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Anil borrows Rs 2 lakhs at an interest rate of 8% per annum, compounded half-yearly. He repays Rs 10320 at the end of the first year and closes the loan by paying the outstanding amount at the end of the third year. Then, the total interest, in rupees, paid over the three years is nearest to

  1. A.

    45311

  2. B.

    51311

  3. C.

    33130

  4. D.

    40991

Answer

B

Explanation

Principal P=200,000P = 200,000. Interest rate per half-year =4%=0.04= 4\% = 0.04.

At the end of Year 1 (2 half-years): A1=200,000×(1.04)2=200,000×1.0816=216,320A_1 = 200,000 \times (1.04)^2 = 200,000 \times 1.0816 = 216,320

Anil repays Rs. 10,320. Outstanding principal for remaining 2 years =216,320−10,320=206,000= 216,320 - 10,320 = 206,000.

At the end of Year 3 (after 4 more half-years): A2=206,000×(1.04)4=206,000×1.16985856≈240,991A_2 = 206,000 \times (1.04)^4 = 206,000 \times 1.16985856 \approx 240,991

Total amount paid =10,320+240,991=251,311= 10,320 + 240,991 = 251,311. Total interest paid =251,311−200,000=51,311= 251,311 - 200,000 = 51,311.

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