Gopal borrows Rs 1,00,000 from a bank at 10% p.a. simple interest and clears…

2026

Gopal borrows Rs 1,00,000 from a bank at 10% p.a. simple interest and clears the debt in five years. If the installments paid at the end of the first, second, third and fourth years to clear the debt are Rs 10,000, Rs 20,000, Rs 30,000 and Rs 40,000 respectively, what amount should be paid at the end of the fifth year to clear the debt?

  1. A.

    Rs.20,000

  2. B.

    Rs.24,500

  3. C.

    Rs.30,000

  4. D.

    Rs.35,900

Attempted by 5 students.

Show answer & explanation

Correct answer: C

In simple-interest debt/instalment problems, the interest for each year is charged only on the principal still outstanding at the START of that year (never on the original loan amount or on interest already accrued). A yearly instalment repays only the principal component; because plain simple interest never itself compounds, the interest charged in every year keeps accruing separately until it is actually paid. So the amount needed to fully close the debt in the final year equals whatever principal is still outstanding (if any) PLUS the total interest that has accrued but not yet been paid.

  1. Year 1: Interest = 10% of Rs 1,00,000 = Rs 10,000. Paying the Rs 10,000 instalment reduces the outstanding principal to Rs 90,000.

  2. Year 2: Interest = 10% of Rs 90,000 = Rs 9,000. Paying the Rs 20,000 instalment reduces the outstanding principal to Rs 70,000.

  3. Year 3: Interest = 10% of Rs 70,000 = Rs 7,000. Paying the Rs 30,000 instalment reduces the outstanding principal to Rs 40,000.

  4. Year 4: Interest = 10% of Rs 40,000 = Rs 4,000. Paying the Rs 40,000 instalment reduces the outstanding principal to Rs 0.

By the end of the fourth year the principal is fully repaid, but the interest charged in each of those four years (Rs 10,000 + Rs 9,000 + Rs 7,000 + Rs 4,000 = Rs 30,000) has never been settled -- that accumulated interest is exactly what falls due in the fifth year.

Cross-check: adding the first four instalments confirms the principal side -- Rs 10,000 + Rs 20,000 + Rs 30,000 + Rs 40,000 = Rs 1,00,000, the full amount borrowed -- so nothing but the accrued interest remains, independently confirming the Rs 30,000 figure.

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