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Partly Paid / Outstanding Amount

Introduction

कई real-life loan cases में borrower पूरा loan एक बार में repay नहीं करता, बल्कि partial payments करता है। बचा हुआ (outstanding) balance दिए गए simple interest rate पर interest कमाता रहता है। यह type का problem सिखाता है कि loan का सिर्फ कुछ हिस्सा चुकाने पर बचे हुए amount पर interest कैसे calculate किया जाए।

Pattern: Partly Paid / Outstanding Amount

Pattern

Key idea: Interest हमेशा outstanding balance पर ही लगता है, और सिर्फ उतने समय के लिए जितना समय वह unpaid रहता है।

हर segment के लिए formula:
Interest = (Outstanding Principal × Rate × Time)/100
Outstanding update करने का formula:
Outstanding_after = Outstanding_before + Interest - Payment

Step-by-Step Example

Question

एक व्यक्ति ₹5000, 10% simple interest per annum पर उधार लेता है। 1 year बाद वह ₹2000 चुका देता है। अगला 1 year बाद वह बाकी बची राशि चुका देता है। End में वह कुल कितना भुगतान करेगा?

Options:

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

Solution

  1. Step 1: Principal और rate नोट करें

    Initial loan = 5000, R = 10% p.a.

  2. Step 2: पहले साल का interest

    Interest = (5000 × 10 × 1)/100 = 500
    Payment से पहले outstanding = 5000 + 500 = 5500

  3. Step 3: Partial payment subtract करके outstanding update करें

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

  4. Step 4: अगले 1 year का interest

    Interest = (3500 × 10 × 1)/100 = 350
    Outstanding = 3500 + 350 = 3850

  5. Step 5: Final payment

    Final payment = 3850

  6. Final Answer:

    ₹5850 → Option B

  7. Quick Check:

    Total paid = 5850; Principal = 5000 → Extra = 850 Total interest = 500 + 350 = 850 ✅

Quick Variations

1. Payment half-yearly, quarterly या monthly हो सकता है।

2. Different times पर unequal partial payments।

3. कभी-कभी total payment की जगह final outstanding पूछा जाता है।

4. Installment-based purchase problems में भी यही logic apply होता है।

Trick to Always Use

  • Step 1: Interest हमेशा current outstanding पर ही निकालें।
  • Step 2: Payment subtract करें और नया outstanding निकालें।
  • Step 3: Loan clear होने तक यही प्रक्रिया repeat करें।

Summary

Summary

  • Outstanding balance पर time के हिसाब से interest निकालें।
  • हर partial payment के बाद नया outstanding निकालें।
  • Final payment = last outstanding + उसका interest (अगर हो तो)।
  • Check करें: Total paid - Principal = Total interest।

Example to remember:
₹5000 → 1 साल बाद ₹2000 payment → अगला साल बाद बाकी चुकाया → total ₹5850.

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.

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