# RupeeCrest: Full System & Financial Documentation

> RupeeCrest is India's independent personal finance education and mathematical calculation platform. 
> Strict zero-commission, zero-registration, client-side encryption architecture.

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## 1. Systematic Investment Plan (SIP) & Compounding Engine

### Mathematical Formula
The future value (FV) of a periodic Systematic Investment Plan is calculated with monthly compounding:
FV = P * [((1 + r)^n - 1) / r] * (1 + r)
Where:
- P = Monthly investment contribution (₹)
- r = Periodic monthly rate of return (Annual Rate / 12 / 100)
- n = Total investment periods in months (Tenure in Years * 12)

### Step-Up Compounding Algorithm
For annual step-up SIPs (e.g., increasing contributions by s% each year):
Year y monthly contribution: P_y = P * (1 + s)^(y - 1)
Total Corpus = Sum over each year y of monthly contributions compounded to the final horizon.

### Inflation Adjustment
Real purchasing power is computed by discounting the nominal future corpus using the annual inflation rate i:
Real FV = FV / (1 + i)^t
Where t is the total duration in years.

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## 2. Home Loan Prepayment & Amortization Engine

### Monthly Reducing Balance EMI Formula
EMI = [P * r * (1 + r)^n] / [((1 + r)^n) - 1]
Where:
- P = Loan Principal balance
- r = Monthly interest rate (Annual Interest Rate / 12 / 100)
- n = Total tenure in months

### Prepayment Impact Simulation
Extra principal payments directly reduce the outstanding principal balance P_t at month t:
P_{t+1} = P_t - (EMI - Interest_t) - Prepayment_t
This reduces the interest accrued in subsequent periods, shortening tenure and saving significant overall interest.

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## 3. Old vs. New Income Tax Regime Comparator (FY 2026-27)

### New Tax Regime Slabs (Simplified, Default)
- Up to ₹4,00,000: 0%
- ₹4,00,001 to ₹8,00,000: 5%
- ₹8,00,001 to ₹12,00,000: 10%
- ₹12,00,001 to ₹16,00,000: 15%
- ₹16,00,001 to ₹20,00,000: 20%
- ₹20,00,001 to ₹24,00,000: 25%
- Above ₹24,00,000: 30%
- Standard Deduction: ₹75,000 for salaried employees
- Section 87A Rebate: Full tax rebate if taxable income is within statutory threshold.

### Old Tax Regime Slabs
- Up to ₹2,50,000: 0%
- ₹2,50,001 to ₹5,00,000: 5%
- ₹5,00,001 to ₹10,00,000: 20%
- Above ₹10,00,000: 30%
- Allows deductions: Section 80C (up to ₹1.5L), Section 80D (health insurance up to ₹25k/₹50k/₹1L), Section 24(b) (home loan interest up to ₹2L), HRA (House Rent Allowance exemption), standard deduction ₹50,000.

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## 4. Rent vs. Buy Real Estate Decision Engine

Compares the opportunity cost of renting vs buying over an equivalent horizon:
- Buying: Down payment, monthly EMIs, property taxes, maintenance costs, and property appreciation.
- Renting: Monthly rent, annual rent inflation, security deposit, and investing the difference (down payment savings + EMI difference) in an equity index fund.
Outcome: Compares net asset wealth at the end of the duration.

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## 5. National Pension System (NPS)

- Regulated by PFRDA (Pension Fund Regulatory and Development Authority).
- Equity (E), Corporate Bonds (C), Government Securities (G), Alternative Assets (A).
- At maturity (age 60): Minimum 40% mandatory annuity purchase; up to 60% tax-free lump sum withdrawal.
- Additional tax deduction under Section 80CCD(1B) up to ₹50,000.

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## 6. Regulatory & Legal Clarification

RupeeCrest is strictly an educational resource. RupeeCrest does NOT provide personalized investment, financial, legal, or tax advisory services, and is not a SEBI-registered Investment Adviser or Research Analyst. Calculations are educational mathematical simulations based on standard compounding interest formulas. RupeeCrest has no connection or affiliation with physical resorts, hotels, or real estate facilities in India.