Question

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

Accepted Answer

B. Principal $P = 200,000$. Interest rate per half-year $= 4\% = 0.04$. At the end of Year 1 (2 half-years): $$A_1 = 200,000 	imes (1.04)^2 = 200,000 	imes 1.0816 = 216,320$$ Anil repays Rs. 10,320. Outstanding principal for remaining 2 years $= 216,320 - 10,320 = 206,000$. At the end of Year 3 (after 4 more half-years): $$A_2 = 206,000 	imes (1.04)^4 = 206,000 	imes 1.16985856 \approx 240,991$$ Total amount paid $= 10,320 + 240,991 = 251,311$. Total interest paid $= 251,311 - 200,000 = 51,311$.

Compound interest with partial repayment

Explanation

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