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. 

Step 1: Loan Amount After First Year

At the conclusion of the first year, the total amount can be calculated as follows:

\(200000 \times \frac{104}{100} \times \frac{104}{100} = 216320\)

Thus, after one year, the total amount due becomes Rs 216,320.

Step 2: Repayment at the End of Year 1

At the end of the first year, Anil repays Rs 10,320. Therefore, the remaining outstanding balance is:

Outstanding balance = Rs 216,320 - Rs 10,320 = Rs 206,000.

Step 3: Loan Amount After Two More Years

The interest will continue to be charged on the outstanding balance of Rs 206,000 for a further two years. The total amount after three years is calculated as:

\(206000 \times \left(\frac{104}{100}\right)^4 = 240990.86\)

So, the total amount due at the end of the third year is Rs 240,990.86.

Step 4: Interest Accrued During Two Years

The interest accrued over the next two years is:

\(240990.86 - 206000 = 34990.86\)

The total interest accumulated over the three years is the sum of the interest for the first year and the next two years:

\(34990.86 + 16320 = 51311\)

Conclusion

The total interest accumulated over the three years is Rs 51,311.