Your home represents the largest asset most people will ever own. Beyond providing shelter and security, your primary residence contains significant financial potential that savvy investors can strategically leverage. Using home equity to purchase investment properties has become an increasingly popular wealth-building strategy for ambitious real estate investors looking to accelerate portfolio growth without waiting years to save additional capital.
According to Stock Picks Guru’s real estate analysis, homeowners today sit on unprecedented equity—the Federal Reserve reports that average home equity exceeds $240,000 for Americans with mortgages. This equity, accumulated through years of mortgage payments and potential property appreciation, represents accessible capital that can fund investment property acquisitions, generate additional income streams, and compound wealth substantially.
However, leveraging home equity for investment purposes requires careful strategy, thorough understanding of available financing mechanisms, and honest assessment of risk tolerance. This comprehensive guide explores every dimension of using home equity for investment property purchases: available financing options, strategic advantages, substantial risks, tax implications, and the decision framework to determine whether this approach aligns with your financial goals.
What Is Home Equity and How Much Do You Have?
Understanding Home Equity Fundamentals
Home equity represents the difference between your property’s current market value and the outstanding mortgage balance. As you make monthly mortgage payments, you build equity through principal repayment. Additionally, when your home appreciates in value, you build equity through property appreciation.
Example of home equity calculation:
- Current home market value: $500,000
- Outstanding mortgage balance: $300,000
- Home equity: $200,000
This $200,000 in equity represents accumulated wealth—both from principal paid down over mortgage payments and from potential property appreciation. Unlike equity trapped in retirement accounts, home equity can be accessed relatively quickly through financing mechanisms.
Most lenders will allow you to borrow against 80-90% of your home’s total value. So if your home is worth $500,000, you could potentially borrow against up to $400,000-$450,000 (after accounting for your existing mortgage). The difference between this borrowing capacity and your existing mortgage balance is your accessible equity.
Calculating accessible equity:
- Home value: $500,000
- Lender maximum LTV (80%): $400,000
- Current mortgage: $300,000
- Accessible equity: $100,000
How to Determine Your Home’s Current Value
Before accessing home equity, you need an accurate understanding of your property’s current market value. Several methods exist:
Professional Appraisal: A licensed appraiser provides an official valuation. Cost: $300-$600. This is the most accurate method and typically required by lenders.
Comparative Market Analysis (CMA): A real estate agent analyzes comparable properties recently sold in your area. Generally free when obtained from an agent, though accuracy depends on market conditions and property specificity.
Online Valuation Tools: Zillow, Redfin, and other platforms provide instant estimates using algorithm-based data. These tools are free and useful for preliminary estimates, but typically less accurate than appraisals, with typical error margins of 5-15%.
Tax Assessment: Your county tax assessment provides an official value, though assessments often lag market conditions and may not reflect true market value.
For accessing significant home equity through formal financing, lenders will require a professional appraisal. Budget accordingly when planning your equity access timeline.
FINANCING OPTIONS – HOW TO ACCESS YOUR HOME EQUITY
Home Equity Line of Credit (HELOC)
A HELOC functions as a flexible credit line secured by your home’s equity. Once approved, you draw funds as needed up to your credit limit, paying interest only on the amount borrowed.
HELOC Characteristics:
- Flexibility: Draw funds only when needed
- Variable Interest Rate: Typically prime rate + margin (adjustable)
- Draw Period: Usually 5-10 years to access funds
- Repayment Period: 10-20 years after draw period ends
- Approval Process: Relatively quick, typically 1-2 weeks
- Interest Deductibility: Generally deductible if funds used for home improvement or investment property acquisition
HELOC Advantages:
- Exceptional flexibility—borrow only what you need when you need it
- Lower initial costs compared to traditional second mortgages
- Variable rates often lower than fixed-rate alternatives during early years
- Can establish the credit line and access it strategically over time
HELOC Disadvantages:
- Rate adjusts with market conditions—payments can increase substantially during rising rate environments
- Draw period limitations—if lender discontinues the line, you cannot access additional funds
- Requires disciplined borrowing—the flexibility can encourage overextension
- Payment uncertainty—variable rates create budget uncertainty
HELOC Use Case: Ideal for investors planning gradual property portfolio expansion over several years, or those wanting to maintain flexibility in accessing capital.
Home Equity Loan (Fixed-Rate)
A home equity loan is a traditional second mortgage offering a fixed interest rate and fixed monthly payment over a set term (typically 5-30 years).
Home Equity Loan Characteristics:
- Fixed Interest Rate: Locked in at approval
- Lump Sum Distribution: Receive all approved funds upfront
- Fixed Monthly Payment: Predictable payments for entire loan term
- Approval Process: 1-3 weeks, more rigorous underwriting than HELOC
- Interest Deductibility: Generally deductible for investment property acquisition
Home Equity Loan Advantages:
- Rate certainty—payment obligations remain constant regardless of market conditions
- Full capital availability immediately—ideal for investors ready to deploy capital
- Typically lower interest rates than HELOCs for the initial fixed period
- Simpler structure—traditional loan mechanics most borrowers understand
Home Equity Loan Disadvantages:
- No flexibility—borrow entire amount upfront even if not immediately needed
- Closing costs typically higher than HELOCs (typically 2-5% of loan amount)
- Rate fixed higher than initial HELOC rates, though stable
- Regular monthly payments required even during financial challenges
Home Equity Loan Use Case: Ideal for investors ready to immediately deploy capital into investment properties, or those prioritizing payment stability over flexibility.
Cash-Out Refinance
A cash-out refinance replaces your existing mortgage with a new, larger mortgage, providing the difference as cash proceeds.
Cash-Out Refinance Characteristics:
- Single Mortgage: Replaces existing mortgage entirely
- Lower Interest Rate Potential: New rate may be lower than existing mortgage rate
- Larger Balance: New mortgage includes original balance plus additional borrowed amount
- Lump Sum Distribution: Receive all cash proceeds upfront
- Approval Timeline: 2-4 weeks
Cash-Out Refinance Advantages:
- Potential rate improvement—if current rates are lower than original mortgage rate
- Single mortgage simplifies monthly payments
- May offer lower rates than HELOC or home equity loans
- Larger amounts available compared to some other financing mechanisms
Cash-Out Refinance Disadvantages:
- Resets mortgage clock—returns you to 30-year amortization (unless you obtain shorter-term refinance)
- Increases total mortgage debt substantially
- Closing costs significant—typically 2-5% of new loan amount
- Refinancing risk—rates may increase, making refinancing unfavorable during application process
Cash-Out Refinance Use Case: Ideal when current mortgage rates are substantially lower than original mortgage rate, or when investor needs significant capital and wants simplified single-mortgage structure.
STRATEGIC ADVANTAGES – WHY USE HOME EQUITY FOR INVESTMENT PROPERTY

Leverage Accelerates Wealth Building
Using home equity to purchase investment properties amplifies wealth-building potential through leverage. Rather than waiting years to save additional down payment capital, you deploy existing home equity immediately.
Example leverage comparison:
Strategy 1 – Saving Without Leverage:
– Current home equity: $200,000
– Annual savings capacity: $30,000
– Time to accumulate second property down payment: 3-4 years
– Properties owned after 5 years: 1
Strategy 2 – Leverage with HELOC:
– Current home equity: $200,000
– HELOC on $150,000 immediately
– Down payment on second property: $150,000 (plus reserves)
– Properties owned after 5 years: 2-3
The leverage strategy potentially doubles or triples portfolio growth within the same timeframe. This acceleration compounds significantly over decades.
Tax Deductibility of Interest
Interest paid on home equity debt used for investment property acquisition is generally tax-deductible, reducing your effective borrowing cost.
Tax deduction example:
– Home equity loan: $200,000 at 8.5% interest
– Annual interest expense: $17,000
– Tax bracket: 32% federal
– Tax deduction value: $5,440 annually
– Effective interest rate after tax benefit: 6.8%
This tax deductibility substantially improves the economics of leverage compared to other financing mechanisms. Always consult a tax professional regarding your specific situation and documentation requirements.
Access to Capital Without Disrupting Primary Residence
HELOCs and home equity loans allow you to access capital while maintaining your existing mortgage structure. You don’t refinance your primary residence mortgage—you simply tap equity through secondary financing.
This approach offers stability: your primary residence mortgage terms remain unchanged, and you don’t risk rate changes on the larger balance.
Improved Investment Property Financing Terms
When acquiring investment properties, stronger down payments (20%+ rather than 10-15%) often provide better financing terms on the property’s mortgage itself:
- Lower interest rates (often 0.25-0.75% lower)
- Eliminated PMI (private mortgage insurance)
- Better loan programs available
- More competitive purchase power
By using home equity for down payment, you simultaneously improve both your borrowing cost on the primary residence equity and your financing terms on the investment property.
SUBSTANTIAL RISKS – WHY THIS STRATEGY REQUIRES CAUTION
Primary Risk: Securing Investment Debt with Your Primary Residence
The most critical risk in using home equity for investment property acquisition is straightforward: you’re pledging your primary residence as security for investment debt. If investments underperform and you cannot meet debt obligations, you risk foreclosure on your family home.
Real-world scenario:
- You borrow $200,000 against home equity
- Real estate market declines 20%
- Investment property rental income insufficient to cover debt
- You cannot refinance due to negative equity position
- Foreclosure becomes possible
This risk distinguishes home equity leverage from other investment financing. You’re not just risking investment property equity—you’re risking housing stability.
Interest Rate Risk with HELOCs
HELOC interest rates adjust with market conditions. During the 2021-2024 period, borrowers with HELOCs saw rates increase substantially:
HELOC Rate History:
- Early 2021: Average HELOC rate 3.5%
- Late 2023: Average HELOC rate 9.0%
- Early 2024: Average HELOC rate 8.5%
A borrower with a $200,000 HELOC saw annual interest payments increase from $7,000 to $18,000—an $11,000 annual increase. This payment shock can devastate investment returns if not carefully planned.
Negative Equity Risk
If your home value declines while you have multiple mortgages outstanding, you can quickly slip into negative equity (owing more than the property is worth). This situation constrains your financial flexibility and prevents refinancing or selling without accepting a loss.
Negative equity scenario:
- Home value: $500,000; Mortgage: $300,000; HELOC: $150,000 (total debt: $450,000)
- Home value declines: $400,000 (20% decline)
- Total debt: $450,000 still outstanding
- Negative equity: $50,000
- Result: Cannot refinance, limited selling options
Real Estate Market Risk
Investment properties acquired using home equity leverage perform poorly if:
- Rental markets soften and rents decline
- Property requires unexpected major repairs
- Tenant defaults on rent
- Property doesn’t appreciate as anticipated
These risks exist with all real estate investments, but using home equity increases the stakes—poor investment performance directly threatens your primary residence.
Overleveraging Risk
The accessibility of home equity can encourage overleveraging—borrowing more than prudent based on actual rental income and financial capacity.
Overleveraging example:
- You have $250,000 accessible home equity
- Lender approves $200,000 HELOC
- You borrow $200,000 for investment property down payment
- Combined with own down payment, purchase $400,000 property
- Rental income: $2,000/month
- Monthly debt service (both mortgages): $3,200/month
- Monthly shortfall: $1,200
- Result: Unsustainable debt servicing, forced selling
Opportunity Cost of Leverage
While leverage amplifies gains during strong market periods, it amplifies losses during downturns. Additionally, paying interest on borrowed capital reduces returns—rental income must exceed debt service before generating actual returns.
Leverage mathematics during downturn:
- Property value: $400,000 purchased with $100,000 down (20%)
- Market decline: 15%
- Property value: $340,000
- Outstanding debt: $300,000
- Equity: $40,000 (down from $100,000)
- Loss on equity: 60%
Without leverage, a 15% price decline would have reduced a cash-purchased property’s value from $400,000 to $340,000, a $60,000 loss on a $100,000 investment (60% loss). The same percentage price decline affects leveraged investments more severely.
TAX IMPLICATIONS AND DEDUCTIBILITY
Interest Deductibility Requirements
Interest on home equity debt is tax-deductible under specific conditions:
Requirements for interest deductibility:
- Funds must be used for home improvement, education, investment purposes, or business
- Funds used to acquire an investment property explicitly qualify
- Documentation must clearly establish the connection between borrowed funds and investment property acquisition
- Total debt cannot exceed the lesser of: home fair market value minus existing mortgages, or original purchase price plus home improvements
Mortgage Interest Deduction vs. Investment Interest Deduction
Home equity interest used for investment property acquisition receives treatment as “investment interest” rather than “mortgage interest,” with important implications:
Mortgage Interest Deduction:
– Deductible without limitation for interest on principal residence debt
– Applies to first $750,000 of home debt (married filing jointly)
Investment Interest Deduction:
– Deductible only to the extent of net investment income
– Net investment income includes rental income, but offsets exist (expenses reduce deductibility)
– Excess investment interest can be carried forward indefinitely
Example:
– Home equity loan interest used for investment property: $15,000
– Rental income from all properties: $40,000
– Rental expenses: $25,000
– Net investment income: $15,000
– Investment interest deductible: $15,000 (fully deductible)
If net investment income were $10,000, only $10,000 of the $15,000 interest would be deductible in that year, with $5,000 carried forward.
Passive Loss Limitations
Rental income and losses from investment properties face passive loss limitations. You can deduct up to $25,000 in passive losses annually against active income if you actively participate in property management—though this phases out at higher incomes.
These limitations reduce the tax benefits of investment property ownership compared to active business income, which is important to consider when evaluating home equity leverage returns.
Documentation and Record-Keeping
The IRS requires clear documentation demonstrating that borrowed funds were specifically used for investment property acquisition. Maintain:
– Loan documentation showing the stated purpose
– Property closing documents
– Bank records showing fund transfers
– Property records establishing connection between borrowed funds and property acquisition
Failure to document properly may result in interest deductibility denial despite legitimate investment use.
CALCULATING RETURNS AND ASSESSING FINANCIAL FEASIBILITY
The Investment Return Framework
When using home equity for investment property acquisition, you must ensure that investment returns exceed financing costs, accounting for all expenses:
Return formula:
Gross rental income
Minus: Property expenses (maintenance, insurance, property tax, HOA)
Minus: Vacancy allowance (typically 5-8%)
Minus: Mortgage principal and interest (both primary home equity debt and property mortgage)
Equals: Net cash flow
This net cash flow must be positive to justify leverage. Additionally, you should model several scenarios:
Scenario 1 – Base Case:
– Expected rental income based on current market
– Anticipated expenses based on property inspection
– Current interest rates
Scenario 2 – Stress Case:
– Rental income 15% below market (higher vacancy, lower rents)
– Expenses 20% above estimate (unexpected repairs)
– Interest rates 2% higher than current rates
Scenario 3 – Severe Downturn:
– Rental income 30% below market
– Expenses 30% above estimate
– Interest rates 3% higher than current rates
Even the severe downturn scenario should show manageable negative cash flow that you can sustain from other income sources.
Cash Reserve Requirements
Before accessing home equity for investment property, ensure adequate financial reserves:
Recommended minimum reserves:
– 6-12 months of all debt obligations (primary mortgage, HELOC, investment property mortgage)
– 6-12 months of investment property expenses
– Separate emergency fund for primary residence maintenance
Many investors under-reserve, then face financial stress when inevitable maintenance or vacancy occurs. Conservative reserve management protects against foreclosure risk.
Example reserve calculation:
– Primary home mortgage: $2,000/month
– HELOC payment: $1,200/month
– Investment property mortgage: $1,500/month
– Investment property expenses: $800/month
– Total monthly obligations: $5,500
– Recommended 12-month reserve: $66,000
– Actual liquid reserves: Should maintain this amount in savings
Debt Service Coverage Ratio Analysis
Professional real estate investors evaluate properties using debt service coverage ratio (DSCR)—net operating income divided by total debt service.
DSCR formula:
Net operating income (rental income minus expenses)
Divided by: Total annual debt service (principal + interest payments)
DSCR interpretation:
– 1.25+ : Strong property, sustainable debt
– 1.0-1.25: Adequate, but limited margin for error
– Below 1.0: Negative cash flow (expenses exceed income)
Properties with DSCR below 1.25 should concern investors using home equity leverage—insufficient margin for unexpected expenses or vacancy.
BEST PRACTICES AND RISK MITIGATION STRATEGIES
Conservative Equity Access
Rather than maxing out your accessible equity, consider accessing only 70-75% of available equity. This buffer protects against:
- Home value declines (preserves positive equity cushion)
- Future refinancing needs (maintains accessible equity for emergencies)
- Rate adjustment shock on HELOCs (payment flexibility if rates rise substantially)
Maintain Strong Cash Reserves
The most critical risk mitigation is maintaining adequate reserves. Unexpected property repairs, tenant default, or market downturns shouldn’t force you into distressed selling or foreclosure.
Reserve targets:
- Minimum: 6 months of total obligations
- Optimal: 12 months of total obligations
- Emergency buffer: Additional 3-6 months
Interest Rate Risk Management
If using HELOC, manage rate adjustment risk:
HELOC rate management strategies:
- Monitor rate environment—refinance to fixed-rate home equity loan if rates appear to have peaked
- Cap payments at current rate level when budgeting (assume worst-case scenario)
- Consider fixed-rate home equity loan if you believe rates will rise significantly
Diversification
Avoid concentrating your entire accessible home equity into a single investment property. Consider:
- Accessing equity gradually over time
- Purchasing multiple smaller properties rather than one large property
- Combining home equity leverage with traditional financing
Regular Financial Review
After accessing home equity and acquiring investment property, maintain regular financial review:
Quarterly review should address:
- Current home value (monitor using online tools monthly, professional appraisal annually)
- Investment property performance (rental income, expenses, occupancy)
- Debt-to-equity position (maintain positive position with margin)
- Interest rate environment (monitor refinancing opportunities)
- Cash reserve levels (maintain target levels)
Professional Guidance
Consult professionals before executing this strategy:
Professional consultation:
- CPA/Tax Professional: Ensure proper documentation and tax optimization
- Real Estate Attorney: Review purchase agreements, lease agreements, liability protection
- Financial Advisor: Ensure strategy aligns with overall financial plan
- Real Estate Professional: Validate property valuation, rental market conditions, investment merits
COMMON MISTAKES AND HOW TO AVOID THEM
Mistake 1: Underestimating Expenses
Many investors underestimate investment property expenses, dramatically overestimating cash flow:
Common underestimated expenses:
- Vacancy rate (assuming 100% occupancy)
- Maintenance (ignoring major systems requiring periodic replacement)
- Property management (if not self-managing)
- Insurance and taxes (using outdated figures)
- Utilities (for furnished properties or rentals)
Avoidance strategy: Use 10-15% higher expense estimates than property owner claims. Request 3 years of actual expense history for properties you’re considering. Budget separately for major system replacement (roof, HVAC, plumbing).
Mistake 2: Neglecting to Model Stress Scenarios
Investors often model only optimistic scenarios (strong occupancy, expected rents, current interest rates).
Avoidance strategy: Model the stress scenario where rental income drops 20-30% and expenses increase 15-20%. Ensure that even in the stress scenario, cash flow doesn’t require constant reserves supplementation.
Mistake 3: Deploying All Capital Immediately
Rather than spreading capital deployment over time, some investors borrow the maximum amount and immediately purchase, leaving no flexibility.
Avoidance strategy: Consider accessing capital in stages. Use HELOC to establish funding, then deploy over 12-24 months as opportunities arise. This approach provides flexibility and reduces timing risk.
Mistake 4: Ignoring Interest Rate Risk with HELOCs
Borrowers often accept HELOC rates without considering adjustment risk, then face payment shock when rates rise.
Avoidance strategy: When accepting HELOC offer, immediately model the impact of rates increasing 2-3%. If you cannot sustain the higher payment, consider fixed-rate home equity loan instead.
Mistake 5: Inadequate Reserve Funding
The most common path to foreclosure is inadequate reserves when unexpected expenses or vacancy occur.
Avoidance strategy: Before accessing home equity, build reserve accounts totaling 12 months of all obligations. Don’t deploy all available capital—preserve emergency access.
GETTING STARTED: WHAT IS HOME EQUITY?
Your home is likely your biggest financial asset. Beyond providing shelter, it holds significant hidden wealth that smart investors can tap into. Home equity is simply the difference between what your home is worth and what you still owe on your mortgage. For example, if your home is valued at $500,000 and your mortgage balance is $300,000, you have $200,000 in home equity—real money that could work for you.
The good news? Most homeowners today have more equity than ever before. Rising property values and years of mortgage payments mean you could have access to a substantial amount of capital right now. The question isn’t whether you have home equity—it’s whether you’ll use it strategically to build wealth.
HOW TO ACCESS YOUR HOME EQUITY
Home Equity Line of Credit (HELOC)
A HELOC works like a credit card backed by your home. Once approved, you draw money when you need it, up to your credit limit. You only pay interest on what you actually borrow. This flexibility makes HELOCs popular for investors who want to purchase multiple properties over time. The downside? Interest rates adjust with the market, so your payments can increase if rates rise.
Home Equity Loans
Unlike a HELOC, a home equity loan gives you a lump sum upfront with a fixed interest rate. Your payments stay the same every month. This predictability appeals to investors who know exactly how much capital they need and want certainty about their monthly obligations. The tradeoff is less flexibility—you get all the money at once, whether you’re ready to deploy it immediately or not.
Cash-Out Refinance
With a cash-out refinance, you replace your existing mortgage with a larger one and pocket the difference. This works best when current interest rates are lower than your original mortgage rate. You end up with one mortgage instead of two, which simplifies things. However, this approach resets your mortgage clock, potentially adding years of payments.
WHY SMART INVESTORS USE HOME EQUITY
Speed Up Your Wealth Building
Saving for a second property down payment might take years. Using home equity lets you access capital immediately. Instead of waiting 3-4 years to save $150,000, you could own your second investment property next year. This acceleration compounds over decades, potentially turning a comfortable retirement into genuine wealth.
Tax Advantages
Interest you pay on home equity borrowed for investment property purchases is tax-deductible. On a $200,000 loan at 8.5% interest, that’s $17,000 annually—potentially worth thousands in tax savings depending on your tax bracket. This reduces your actual borrowing cost significantly.
Better Financing Terms
When you can put 20% or more down on an investment property, lenders offer better mortgage rates. You might save 0.5% or more on the property’s mortgage, plus you avoid private mortgage insurance (PMI). These advantages compound the benefits of using home equity as your down payment.
UNDERSTAND THE REAL RISKS
Your Home Is Now on the Line
This is the critical reality: if your investment property fails and you can’t pay the debt, you risk foreclosure on your primary residence. You’re not just risking the investment—you’re risking where your family lives. This isn’t a risk with regular investment property financing. Take it seriously.
Interest Rate Shocks
HELOC rates move with the market. A borrower with a $200,000 HELOC saw rates jump from 3.5% in early 2021 to 9% by late 2023. That’s an extra $11,000 in annual interest payments. If your investment income hasn’t grown that much, this shock can hurt. Fixed-rate loans avoid this problem.
Market Downturns
Real estate doesn’t always go up. If the market drops 20% and your investment property rental income falls short of expenses, you’re stuck with negative cash flow. Worse, if your home value also drops, you might end up with negative equity—owing more than your properties are worth. This severely limits your options.
THE MATH BEHIND SUCCESS
Make Sure the Numbers Work
Before borrowing anything, calculate whether your investment property rental income covers all expenses and debt payments. Your monthly rent minus all expenses (including both mortgages) should be positive. If rental income is $2,000 monthly but debt payments total $2,500, you’re paying $500 monthly out of pocket. That’s unsustainable leverage.
Conservative Planning Wins
Successful investors don’t access 100% of their available equity. They access 70-75%, keeping a buffer. They model what happens if rents drop 20% and expenses jump 30%. They maintain 12 months of reserves for all obligations. This conservative approach protects against the inevitable surprises that hit every real estate investor.
BUILDING YOUR WEALTH STRATEGY
Start by getting your home professionally appraised to know exactly what equity you have. Next, compare financing options from multiple lenders—HELOC rates and terms vary significantly. Then carefully evaluate each investment property before committing capital. Don’t rush. The best deals come to patient investors.
Once you purchase your first investment property with home equity, let it appreciate. In 3-5 years, refinance that property and pull your home equity back out. Use recovered equity for your next property. This cycle repeats, building a leveraged portfolio gradually over time. This disciplined approach compounds wealth without overleveraging at any single point.
IS THIS STRATEGY RIGHT FOR YOU?
Home equity leverage works for investors with stable income, manageable debt, reserve capital, and real estate knowledge. It’s dangerous for those with unstable jobs, high existing debt, no reserves, or no investment experience. Most importantly, you must be comfortable with the reality: your family home backs this strategy.
Used wisely, home equity becomes a powerful tool for building substantial real estate wealth over decades. Access conservative amounts, maintain generous reserves, consult professionals, and execute with discipline. The most successful investors didn’t maximize their leverage—they optimized it. Your financial security depends on the same wisdom.




























