Financing, Valuation, and Real Estate Mathematics
Loan basics
Loan-to-value (LTV) is the loan amount divided by the purchase price or appraised value, whichever is lower. Down payment is the complement. Points are prepaid interest: one point equals 1% of the loan amount. Conventional loans with less than 20% down usually require private mortgage insurance, which must terminate at 78% LTV by amortization schedule and may be cancelled at 80% on request. FHA loans carry mortgage insurance premiums; VA loans typically require no down payment but charge a funding fee. Payment is quoted as PITI - principal, interest, taxes, insurance. Traditional qualifying ratios hover near 28/36 for conventional and 31/43 for FHA, though automated underwriting has loosened these. New Jersey buyers may use NJHMFA first-time buyer programs. Federal disclosure rules (RESPA/TRID, TILA, ECOA) govern the Loan Estimate, Closing Disclosure, and fair lending.
Valuation
Three approaches: sales comparison (best for residential resale), cost (replacement cost minus depreciation plus land value - best for special-purpose property), and income (best for investment property). Income capitalization: Value = NOI ÷ cap rate. Gross rent multiplier: Price ÷ monthly (or annual) gross rent.
Math traps
Watch whether a commission question asks for the total commission, the split, or the listing side's share. Watch whether points are computed on the loan or the price. Watch whether prorations run on 365 or 360 days. Always restate the question in one sentence before calculating.
Worked example
A property produces $60,000 net operating income; comparable sales indicate an 8% cap rate. Value = $60,000 ÷ 0.08 = $750,000. If the buyer pays $750,000 with 20% down, the loan is $600,000 and two points cost $12,000.