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Partly Paid / Outstanding Amount

Introduction

பல நிஜ வாழ்க்கை கடன் நிலைகளில், ஒரு கடனாளி முழு கடனையும் ஒரே முறையில் திருப்பிச் செலுத்தாமல், partial payments செலுத்துகிறார். மீதமுள்ள (outstanding) தொகைக்கு, கொடுக்கப்பட்ட simple interest விகிதத்தில் interest தொடர்ந்து விதிக்கப்படும். இந்த வகை கேள்விகள், கடனின் ஒரு பகுதி மட்டுமே செலுத்தப்பட்டால் interest-ஐ சரியாக எவ்வாறு கணக்கிடுவது என்பதை கற்றுக்கொடுக்கும்.

Pattern: Partly Paid / Outstanding Amount

Pattern

Key idea: repayment வரை உள்ள உண்மையான காலத்திற்கு, எப்போதும் outstanding balance மீது தான் interest விதிக்கப்படுகிறது.

ஒவ்வொரு segment-க்கும் formula:
Interest = (Outstanding Principal × Rate × Time)/100
Outstanding update செய்வது:
Outstanding_after = Outstanding_before + Interest - Payment

Step-by-Step Example

Question

ஒரு மனிதர் ₹5000-ஐ ஆண்டுக்கு 10% simple interest விகிதத்தில் கடன் பெறுகிறார். 1 ஆண்டு முடிவில் அவர் ₹2000 செலுத்துகிறார். மேலும் 1 ஆண்டு கழித்து மீதமுள்ள தொகையை முழுவதும் செலுத்துகிறார். இறுதியில் அவர் செலுத்தும் மொத்த தொகையை காண்க.

Options:

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

Solution

  1. Step 1: Principal மற்றும் rate-ஐ பதிவு செய்யவும்

    Initial loan = 5000, R = ஆண்டுக்கு 10%.

  2. Step 2: முதல் ஆண்டிற்கான interest-ஐ கணக்கிடவும்

    முதல் ஆண்டின் interest = (5000 × 10 × 1)/100 = 500. Payment-க்கு முன் Outstanding = 5000 + 500 = 5500.

  3. Step 3: Partial payment-ஐ கழித்து outstanding-ஐ update செய்யவும்

    1 ஆண்டு முடிவில் Payment = 2000. புதிய outstanding = 5500 - 2000 = 3500.

  4. Step 4: அடுத்த ஆண்டிற்கான interest-ஐ update செய்யப்பட்ட outstanding மீது கணக்கிடவும்

    அடுத்த 1 ஆண்டிற்கான interest = (3500 × 10 × 1)/100 = 350. Outstanding = 3500 + 350 = 3850.

  5. Step 5: இறுதி payment

    2 ஆண்டுகள் முடிவில் செலுத்த வேண்டிய இறுதி தொகை = 3850.

  6. Final Answer:

    ₹5850 → Option B

  7. Quick Check:

    மொத்தம் செலுத்தியது (5850) - Principal (5000) = 850 → மொத்த interest (500 + 350)க்கு சமம். ✅

Quick Variations

1. Payment half-yearly, quarterly அல்லது monthly ஆக இருக்கலாம்.

2. வேறு வேறு நேரங்களில் சமமில்லாத partial payments.

3. சில கேள்விகளில் total payment பதிலாக final outstanding கேட்கப்படும்.

4. Installment-based purchase problems-லிலும் இதை பயன்படுத்தலாம்.

Trick to Always Use

  • Step 1: எப்போதும் தற்போதைய outstanding மீது மட்டும் interest கணக்கிடவும்.
  • Step 2: Due amount-லிருந்து partial payment-ஐ கழிக்கவும்.
  • Step 3: Loan clear ஆகும் வரை புதிய outstanding-ஐ தொடர்ந்து பயன்படுத்தவும்.

Summary

Summary

  • கொடுக்கப்பட்ட காலத்திற்கு outstanding balance மீது interest கணக்கிடவும்.
  • ஒவ்வொரு partial payment-க்கும் பிறகு outstanding-ஐ update செய்யவும்.
  • Final payment = கடைசி outstanding + interest.
  • Check: Total paid - Principal = Total interest.

நினைவில் வைக்க வேண்டிய example:
₹5,000 கடன் → 1 ஆண்டு கழித்து ₹2,000 செலுத்துதல் → அடுத்த ஆண்டு மீதியை செலுத்துதல் → மொத்தம் ₹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

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