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

• A. 33130
• B. 40991
• C. 51311
• D. 51311

Answer 1

The Correct Option is C

Anil takes out a loan of Rs 2 lakhs, with interest compounded every six months at a rate of 8% per year. 
It is also known that at the conclusion of the first year, he repays Rs 10,320, and at the end of the third year, he terminates the debt by making the final payment.
At the conclusion of the first year, the total is \(200000 \times \frac{104}{100} \times \frac{104}{100} = 216320\)
By the time the first year ends, he has paid back 10320 rupees, meaning that 206000 rupees are still outstanding.
Interest will be charged on this outstanding balance for a further two years. 
Thus, after three years, the total is \(206000 \times \frac{104}{100} \times \frac{104}{100} \times \frac{104}{100} \times \frac{104}{100} = 240990.86\)
For these two years, the total interest earned is (240990.86-206000) = 34990.86 rupees. The interest that was accumulated in total over the three years is therefore (34990.86+16320) = 51311 rupees.