0
0

Partly Paid / Outstanding Amount

Introduction

In many real-life loan cases, a borrower does not repay the full loan in one go but makes partial payments. The remaining (outstanding) balance continues to accrue interest at the given simple interest rate. This type of problem teaches how to correctly calculate interest when only part of the loan is repaid.

Pattern: Partly Paid / Outstanding Amount

Pattern

The key idea: Interest is always charged on the outstanding balance for the actual time period until repayment.

Formula for each segment:
Interest = (Outstanding Principal × Rate × Time)/100
Update outstanding:
Outstanding_after = Outstanding_before + Interest - Payment

Step-by-Step Example

Question

A man borrows ₹5000 at 10% simple interest per annum. After 1 year, he pays ₹2000. He clears the remaining balance after 1 more year. Find the total amount he pays at the end.

Options:

  • A. ₹5800
  • B. ₹5850
  • C. ₹5900
  • D. ₹6000

Solution

  1. Step 1: Record the principal and rate

    Initial loan = 5000, R = 10% per annum.

  2. Step 2: Calculate interest for the first year

    Interest for first year = (5000 × 10 × 1)/100 = 500. Outstanding before payment = 5000 + 500 = 5500.

  3. Step 3: Subtract the partial payment and update outstanding

    Payment after 1 year = 2000. New outstanding = 5500 - 2000 = 3500.

  4. Step 4: Compute interest on the updated outstanding for the next year

    Interest on 3500 for next 1 year = (3500 × 10 × 1)/100 = 350. Outstanding = 3500 + 350 = 3850.

  5. Step 5: Final payment equals the last outstanding

    Final payment after 2 years = 3850.

  6. Final Answer:

    ₹5850 → Option B

  7. Quick Check:

    Total paid (5850) - Principal (5000) = 850 → equals total interest (500 + 350). ✅

Quick Variations

1. Payment may be done half-yearly, quarterly, or monthly.

2. Partial payments of unequal amounts at different times.

3. Sometimes the final outstanding is asked instead of total payment.

4. Can also be used in installment-based purchase problems.

Trick to Always Use

  • Step 1: Always calculate interest only on the current outstanding.
  • Step 2: Subtract the partial payment from the total due.
  • Step 3: Continue with the new outstanding until loan is cleared.

Summary

Summary

  • Compute interest on outstanding balance for the time period.
  • Update outstanding after each partial payment.
  • Final payment = last outstanding + interest.
  • Check: Total paid - Principal = Total interest charged.

Example to remember:
Borrow ₹5,000 → pay ₹2,000 after 1 year → clear remainder next year → total paid ₹5,850.

Practice

(1/5)
1. A man borrows ₹2000 at 10% simple interest. After 1 year, he pays ₹1000. He clears the balance after 1 more year. Find the total amount he pays.
easy
A. ₹2320
B. ₹2300
C. ₹2400
D. ₹2250

Solution

  1. Step 1: Record principal and rate

    Given P = 2000, R = 10% p.a.

  2. Step 2: Compute interest for the first year and outstanding before payment

    Interest for 1 year = (2000 × 10 × 1)/100 = ₹200. Outstanding before payment = 2000 + 200 = ₹2200.

  3. Step 3: Subtract the partial payment and update outstanding

    First payment = ₹1000 → New outstanding = 2200 - 1000 = ₹1200.

  4. Step 4: Compute interest on the outstanding for the next year

    Interest on ₹1200 for next 1 year = (1200 × 10 × 1)/100 = ₹120. Outstanding (final payment) = 1200 + 120 = ₹1320.

  5. Final Answer:

    ₹2320 → Option A

  6. Quick Check:

    Total interest paid = 2320 - 2000 = ₹320 = 200 + 120 (sum of interests) ✅
Hint: Add interest first, subtract the partial payment, then compute interest on the outstanding for the next period.
Common Mistakes: Subtracting the payment before adding interest for that period.
2. A loan of ₹3000 at 12% simple interest is partly repaid with ₹1000 at the end of 1 year. The balance is paid at the end of the 2nd year. Find the final payment (to two decimals).
easy
A. ₹2600.10
B. ₹2643.20
C. ₹2700.50
D. ₹2500.75

Solution

  1. Step 1: Record principal and rate

    Given P = 3000, R = 12% p.a.

  2. Step 2: Compute interest for first year and outstanding before first payment

    Interest for 1 year = (3000 × 12 × 1)/100 = ₹360. Outstanding before first payment = 3000 + 360 = ₹3360.

  3. Step 3: Subtract the partial payment and update outstanding

    First payment = ₹1000 → New outstanding = 3360 - 1000 = ₹2360.

  4. Step 4: Compute interest on the outstanding for the next year and final payment

    Interest on ₹2360 for 1 year = (2360 × 12 × 1)/100 = ₹283.20. Final payment = 2360 + 283.20 = ₹2643.20.

  5. Final Answer:

    ₹2643.20 → Option B

  6. Quick Check:

    Total paid = 1000 + 2643.20 = 3643.20; total interest = 3643.20 - 3000 = ₹643.20 = 360 + 283.20 ✅
Hint: Always compute interest on the outstanding after the partial payment for the remaining period.
Common Mistakes: Using principal instead of outstanding to compute the second period's interest.
3. ₹4000 is borrowed at 5% simple interest. After 2 years the borrower pays ₹2000. He clears the remaining debt after 1 more year. Find the final payment.
easy
A. ₹2520
B. ₹2500
C. ₹2600
D. ₹2400

Solution

  1. Step 1: Record principal and rate

    Given P = 4000, R = 5% p.a.

  2. Step 2: Compute interest for the first 2 years and outstanding before payment

    Interest for first 2 years = (4000 × 5 × 2)/100 = ₹400. Outstanding before payment = 4000 + 400 = ₹4400.

  3. Step 3: Subtract the partial payment and update outstanding

    Payment after 2 years = ₹2000 → New outstanding = 4400 - 2000 = ₹2400.

  4. Step 4: Compute interest on the outstanding for next year and final payment

    Interest on ₹2400 for 1 year = (2400 × 5 × 1)/100 = ₹120. Final payment = 2400 + 120 = ₹2520.

  5. Final Answer:

    ₹2520 → Option A

  6. Quick Check:

    Total paid = 2000 + 2520 = 4520; total interest = 4520 - 4000 = ₹520 = 400 + 120 ✅
Hint: Compute full interest first, subtract the partial payment, then compute interest on the remaining outstanding.
Common Mistakes: Deducting payment before adding interest for the first period.
4. ₹6000 is borrowed at 10% simple interest. The borrower pays ₹2000 after 1 year and ₹2000 after 2 years. He clears the balance after the 3rd year. Find the final payment.
medium
A. ₹3300
B. ₹3350
C. ₹3366
D. ₹3400

Solution

  1. Step 1: Record principal and rate

    Given P = 6000, R = 10% p.a.

  2. Step 2: Year 1 - compute interest, outstanding before payment and update

    Year 1 interest = (6000 × 10 × 1)/100 = ₹600. Outstanding before payment1 = 6000 + 600 = ₹6600. After payment1 (₹2000) → outstanding = 6600 - 2000 = ₹4600.

  3. Step 3: Year 2 - compute interest, outstanding before payment and update

    Year 2 interest on ₹4600 = (4600 × 10 × 1)/100 = ₹460. Outstanding before payment2 = 4600 + 460 = ₹5060. After payment2 (₹2000) → outstanding = 5060 - 2000 = ₹3060.

  4. Step 4: Year 3 - compute interest on outstanding and final payment

    Year 3 interest on ₹3060 = (3060 × 10 × 1)/100 = ₹306. Final payment = 3060 + 306 = ₹3366.

  5. Final Answer:

    ₹3366 → Option C

  6. Quick Check:

    Total interest = 600 + 460 + 306 = ₹1366; total paid = 2000 + 2000 + 3366 = 7366 = 6000 + 1366 ✅
Hint: After each payment compute outstanding = previous outstanding + interest - payment; final outstanding + interest = final payment.
Common Mistakes: Charging interest on the wrong outstanding amount (e.g., after subtracting payment).
5. ₹8000 is borrowed at 15% simple interest. The borrower pays ₹4000 after 1 year. He clears the remaining balance after 2 more years. Find the final payment.
medium
A. ₹6000
B. ₹6500
C. ₹7000
D. ₹6760

Solution

  1. Step 1: Record principal and rate

    Given P = 8000, R = 15% p.a.

  2. Step 2: Compute interest for the first year and outstanding before payment

    Interest for 1 year = (8000 × 15 × 1)/100 = ₹1200. Outstanding before payment = 8000 + 1200 = ₹9200. After payment (₹4000) → outstanding = 9200 - 4000 = ₹5200.

  3. Step 3: Compute interest on the outstanding for the next 2 years and final payment

    This outstanding remains unpaid for 2 years. Interest for 2 years = (5200 × 15 × 2)/100 = ₹1560. Final payment = 5200 + 1560 = ₹6760.

  4. Final Answer:

    ₹6760 → Option D

  5. Quick Check:

    Total interest = 1200 + 1560 = ₹2760; total paid = 4000 + 6760 = 10,760 = 8000 + 2760 ✅
Hint: Compute interest for each unpaid segment separately and sum to get final outstanding.
Common Mistakes: Charging interest only for 1 year on the remaining balance when it is actually outstanding for multiple years.

Mock Test

Ready for a challenge?

Take a 10-minute AI-powered test with 10 questions (Easy-Medium-Hard mix) and get instant SWOT analysis of your performance!

10 Questions
5 Minutes