Real Estate Mathematics
Percentages, commissions, and points
Commission equals price times rate, and splits are successive multiplications. Points equal a percentage of the loan amount, not the purchase price. Down payment percentage and loan-to-value add to 100 relative to price. Appreciation and depreciation problems use the same base-plus-change structure; always identify the base before applying a rate.
Prorations
Use a consistent day count, usually a 365-day year for taxes in Oregon, and read the contract for whether the seller is charged through the day of closing or the day before. Oregon property taxes are paid in arrears, so at a mid-year closing the seller owes the buyer for the portion of the tax year already used. Rent is paid in advance, so the seller credits the buyer for rent already collected for days the buyer will own.
Area and income math
There are 43,560 square feet in an acre and 640 acres in a section. Price per square foot equals price divided by area. Value equals net operating income divided by cap rate. Gross rent multiplier times rent gives value. Property tax equals assessed value times the rate per thousand, or times mills divided by 1000.
Amortization
Monthly payment uses the monthly rate with the standard annuity formula. Most exam items can be solved with simpler tools: one month's interest equals balance times annual rate divided by 12, and a loan balance can be approximated by capitalizing the payment at the mortgage constant.
Worked example: annual taxes are $3,650, closing is June 30, and the seller pays through the closing day. Day 181 of 365 at $10 per day means the seller owes $1,810, debited to the seller and credited to the buyer.