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TEST: EXACT EXAMPLE FROM PDF (Page 3)
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Given Data:
  Monthly Payment (EMI): TSH 177,697.00
  Annual Interest Rate: 12%
  Monthly Rate (r): 0.01
  Initial Balance (IB): TSH 6,397,076.07
  Remaining Balance (BA): TSH 4,264,712.07

--- Step 1: Calculate Original Principal (PV) ---
  Tenure (n) = IB / EMI = 6,397,076.07 / 177,697.00 ≈ 36 months
  PV = EMI × [1 - (1 + r)^-n] / r
  PV = 177697 × [1 - (1.01)^-36] / 0.01
  PV = TSH 5,350,013.32

--- Step 2: Determine Number of Payments Made (m) ---
  Remaining Payments = BA / EMI = 4,264,712.07 / 177,697.00 = 24
  Payments Made (m) = n - remaining = 36 - 24 = 12

--- Step 3: Calculate Outstanding Principal (Payoff) ---
  Formula: Payoff = PV × [(1 + r)^n - (1 + r)^m] / [(1 + r)^n - 1]
  Payoff = 5,350,013.32 × [(1.01)^36 - (1.01)^12] / [(1.01)^36 - 1]
  (1.01)^36 = 1.43076878
  (1.01)^12 = 1.12682503
  Outstanding Principal = TSH 3,774,886.18

--- Step 4: Calculate Final Payoff Amount ---
  Days Since Last Payment: 7
  Accrued Interest = Principal × (Annual Rate / 365) × Days
  Accrued Interest = 3,774,886.18 × (0.12/365) × 7
  Accrued Interest = TSH 8,687.41

  TOTAL PAYOFF AMOUNT = Principal + Accrued Interest
  TOTAL PAYOFF AMOUNT = 3,774,886.18 + 8,687.41
  TOTAL PAYOFF AMOUNT = TSH 3,783,573.59

--- Comparison with PDF ---
  PDF Expected Outstanding Principal: TSH 3,775,000.00
  Our Calculated Outstanding Principal: TSH 3,774,886.18
  Difference: TSH 113.82


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ADDITIONAL TEST SCENARIOS
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--- Small Loan - 25% Paid ---
  Tenure: 20 months, Payments Made: 5
  Original Principal: TSH 917,600.90
  Outstanding Principal: TSH 702,275.29
  Accrued Interest: TSH 1,924.04
  Total Payoff: TSH 704,199.33

--- Medium Loan - 75% Paid ---
  Tenure: 24 months, Payments Made: 18
  Original Principal: TSH 3,316,581.54
  Outstanding Principal: TSH 879,367.81
  Accrued Interest: TSH 2,891.07
  Total Payoff: TSH 882,258.88

--- Large Loan - Just Started ---
  Tenure: 24 months, Payments Made: 1
  Original Principal: TSH 10,312,117.26
  Outstanding Principal: TSH 9,941,018.73
  Accrued Interest: TSH 20,426.75
  Total Payoff: TSH 9,961,445.48


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SUMMARY
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The Reducing Balance Method has been successfully implemented!
The formula correctly calculates payoff amounts using:
  1. PV = EMI × [1 - (1 + r)^-n] / r (for original principal)
  2. Payoff = PV × [(1 + r)^n - (1 + r)^m] / [(1 + r)^n - 1] (for outstanding principal)
  3. Total Payoff = Outstanding Principal + Accrued Interest

✅ Implementation matches the corrected formulas from the PDF!