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 secured a loan of Rs 2,00,000. The interest is compounded semi-annually at an annual rate of 8%.

Anil repays Rs 10,320 at the end of the first year and settles the entire loan with a final payment at the end of the third year.

Step 1: Loan Balance After Year 1

The total loan amount after the first year is calculated as:

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

Therefore, the outstanding loan amount after one year is Rs 216,320.

Step 2: Repayment at End of Year 1

Anil repays Rs 10,320 at the conclusion of the first year. The revised outstanding balance is:

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

Step 3: Loan Balance After Two Additional Years

Interest continues to accrue on the Rs 206,000 balance for the subsequent two years. The total amount after three years is computed as:

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

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

Step 4: Interest Accrued Over Two Years

The interest accrued during the subsequent two years is:

\(240990.86 - 206000 = 34990.86\)

The total interest accumulated over the entire three-year period is the sum of the interest from the first year and the subsequent two years:

\(34990.86 + 16320 = 51311\)

Conclusion

The aggregate interest accumulated over the three-year period amounts to Rs 51,311.