The Ultimate Loans & EMI Cheatsheet

╔══════════════════════════════════════════════════════════════╗
║                  LOAN SELECTION GUIDE                        ║
╠══════════════════════════════════════════════════════════════╣
║ Buying a house          → Home Loan (longest tenure, lowest) ║
║ Buying a car            → Car Loan (depreciating asset)      ║
║ Medical emergency       → Personal Loan (quick, no collateral)║
║ Higher education        → Education Loan (tax benefit 80E)   ║
║ Business expansion      → Business Loan or LAP               ║
║ Short-term cash need    → Loan against FD/Gold (cheapest)   ║
║ Home renovation         → Top-up on existing home loan       ║
║ Consolidate debt        → Personal Loan (lower than CC rate) ║
╚══════════════════════════════════════════════════════════════╝

import math

def calculate_emi(principal, annual_rate, tenure_months):
    """
    EMI = P × r × (1+r)^n / ((1+r)^n - 1)
    
    P = Principal loan amount
    r = Monthly interest rate (annual_rate / 12 / 100)
    n = Total number of monthly installments
    """
    r = annual_rate / 12 / 100
    n = tenure_months
    
    if r == 0:
        return principal / n
    
    emi = principal * r * (1 + r)**n / ((1 + r)**n - 1)
    return round(emi, 2)

# Example: Home Loan
emi = calculate_emi(5000000, 8.5, 240)  # ₹50L, 8.5%, 20 years
print(f"Monthly EMI: ₹{emi:,.2f}")     # ₹43,391

# Total payment and interest
total_payment = emi * 240
total_interest = total_payment - 5000000
print(f"Total Interest: ₹{total_interest:,.2f}")  # ₹54,13,795
print(f"Total Payment: ₹{total_payment:,.2f}")   # ₹1,04,13,795

def amortization_schedule(principal, annual_rate, tenure_months, months_to_show=12):
    r = annual_rate / 12 / 100
    emi = principal * r * (1+r)**tenure_months / ((1+r)**tenure_months - 1)
    balance = principal
    
    print(f"{'Month':>5} | {'EMI':>12} | {'Interest':>12} | {'Principal':>12} | {'Balance':>14}")
    print("-" * 65)
    
    for month in range(1, months_to_show + 1):
        interest_component = balance * r
        principal_component = emi - interest_component
        balance -= principal_component
        print(f"{month:>5} | ₹{emi:>10,.0f} | ₹{interest_component:>10,.0f} | "
              f"₹{principal_component:>10,.0f} | ₹{balance:>12,.0f}")

amortization_schedule(5000000, 8.5, 240, 6)
# Month 1: EMI ₹43,391 | Interest ₹35,417 | Principal ₹7,975 | Balance ₹49,92,025
# Month 6: EMI ₹43,391 | Interest ₹34,987 | Principal ₹8,404 | Balance ₹49,51,603

def home_loan_eligibility(monthly_income, monthly_obligations, 
                           interest_rate=8.5, tenure_years=20):
    """Calculate max home loan eligible based on income"""
    
    # Banks use FOIR (Fixed Obligation Income Ratio)
    # Max EMI should be 40-50% of monthly income
    max_emi_ratio = 0.50  # Conservative: 50%
    available_income = monthly_income * max_emi_ratio - monthly_obligations
    
    if available_income <= 0:
        return 0
    
    # Calculate max loan from available EMI
    r = interest_rate / 12 / 100
    n = tenure_years * 12
    max_loan = available_income * ((1 + r)**n - 1) / (r * (1 + r)**n)
    
    return round(max_loan)

# Example: ₹1L/month income, ₹15K obligations
loan = home_loan_eligibility(100000, 15000)
# Eligible: ~₹38-45 Lakhs (depending on bank criteria)

Year │ Car Value     │ Loan Balance (₹9L, 9%, 5yr) │ Status
─────┼───────────────┼─────────────────────────────────┼──────────
  0  │ ₹10,00,000    │ ₹9,00,000                      │ Purchase
  1  │ ₹8,00,000     │ ₹7,24,000                      │ Upside down!
  2  │ ₹6,40,000     │ ₹5,39,000                      │ Still negative
  3  │ ₹5,12,000     │ ₹3,44,000                      │ Recovering
  4  │ ₹4,10,000     │ ₹1,39,000                      │ Nearly even
  5  │ ₹3,28,000     │ ₹0                             │ Own it

⚠️  For first 2-3 years, car is worth LESS than the loan!
💡  Consider: Higher down payment (20%+) or shorter tenure (3 yrs)

# FLAT RATE vs REDUCING BALANCE — Hidden Cost Trap

def flat_vs_reducing(principal, flat_rate, tenure_months):
    """Compare flat rate vs reducing balance rate"""
    
    # FLAT RATE calculation (often advertised)
    total_interest_flat = principal * (flat_rate / 100) * (tenure_months / 12)
    emi_flat = (principal + total_interest_flat) / tenure_months
    
    # Convert flat rate to effective reducing balance rate
    # Using IRR approximation
    effective_rate = flat_rate * 1.85  # Rough approximation
    
    total_interest_reducing = 0
    balance = principal
    r = effective_rate / 12 / 100
    emi_reducing = principal * r * (1+r)**tenure_months / ((1+r)**tenure_months - 1)
    
    print(f"Flat Rate {flat_rate}% = Effective Rate ~{effective_rate:.1f}%")
    print(f"EMI (Flat): ₹{emi_flat:,.0f} vs EMI (Reducing): ₹{emi_reducing:,.0f}")
    print(f"Interest (Flat): ₹{total_interest_flat:,.0f}")
    
flat_vs_reducing(500000, 10, 36)
# Flat Rate 10% = Effective Rate ~18.5%
# Always ask for REDUCING BALANCE rate!

def prepayment_impact(principal, annual_rate, tenure_months, 
                       prepayment_amount, prepayment_month=12):
    """
    Calculate impact of making a lump sum prepayment
    """
    r = annual_rate / 12 / 100
    emi = principal * r * (1+r)**tenure_months / ((1+r)**tenure_months - 1)
    
    balance = principal
    total_interest_without = emi * tenure_months - principal
    
    months_saved = 0
    total_interest_with = 0
    
    for month in range(1, tenure_months + 1):
        interest = balance * r
        principal_part = emi - interest
        total_interest_with += interest
        
        if month == prepayment_month:
            balance -= prepayment_amount
            if balance < 0:
                months_saved = tenure_months - month
                break
        
        balance -= principal_part
        if balance <= 0:
            months_saved = tenure_months - month
            break
    
    interest_saved = total_interest_without - total_interest_with
    print(f"Prepayment of ₹{prepayment_amount:,} in month {prepayment_month}")
    print(f"Interest saved: ₹{interest_saved:,.0f}")
    print(f"Months saved: {months_saved}")

prepayment_impact(5000000, 8.5, 240, 500000, 12)
# ₹5L prepayment in year 1 saves ~₹7-8L interest and ~2 years!