PRINTABLE
The formula sheet.
Every formula the twenty math drill types use, with the New York constants exactly as the drills state them. Print it, keep it by the desk, and do the problems until the setup is automatic.
Constants to memorise
1 acre = 43,560 sq ftNYS transfer tax: $2 per $500, rounded upMansion tax: 1% of the whole price at $1,000,000 and up1 mill = $1 per $1,000 of assessed valueTax proration: 365-day year, seller through the day before closingRent proration: 30-day month, closing day belongs to the buyer1 point = 1% of the loan
The twenty problem types
1. Commission splits
Price × Rate = Total commissionTotal ÷ 2 = One sideSide × Agent % = Agent’s shareWhole commission first, then the broker split, then the agent split. Never apply the agent’s % to the full price.
2. Net to seller
Net ÷ (1 − Rate) = Sale priceDivide, never multiply: the commission is charged on the price, not on the net.
3. Tax proration
Annual tax ÷ 365 = Daily rateDays Jan 1 → day before closing × Daily rate = Seller’s shareTaxes in arrears: the seller owes Jan 1 up to, not including, closing day (365-day year).
4. Rent proration
Monthly rent ÷ 30 = Daily rentDays from closing → month end × Daily rent = Credit to buyerRent is paid in advance, so the seller credits the buyer — the opposite direction from taxes (30-day month, closing day belongs to the buyer).
5. NYS transfer tax
Price ÷ $500 → round UP = UnitsUnits × $2 = NYS transfer tax (≈ 0.4%)“Or fraction thereof” = always round up. The seller pays it in New York unless the contract says otherwise.
6. Mansion tax
Price ≥ $1,000,000 → Price × 1% = Mansion taxOn the entire price, not the amount above the threshold — and the buyer pays it.
7. Lot size & acreage
Width × Length = Square feetSquare feet ÷ 43,560 = Acres43,560 square feet in an acre. Memorise it.
8. Price per square foot
Price ÷ Square feet = Price per sq ftGiven any two of the three, you can find the third.
9. LTV & down payment
Price × LTV % = LoanPrice − Loan = Down payment (= Price × (100% − LTV))LTV is the loan as a percent of value; the down payment is the rest.
10. Discount points
Loan × Points % = Cost of points (1 point = 1% of the LOAN)Points are a percentage of the loan, never of the purchase price.
11. Monthly interest
Loan × Annual rate ÷ 12 = One month’s interestInterest is charged on the outstanding balance; month one uses the full loan.
12. Amortization
Loan × Rate ÷ 12 = Month-1 interestPayment − Interest = Principal paidLoan − Principal paid = New balanceEvery payment covers interest first; the rest reduces principal.
13. Property tax
Assessed value ÷ 1,000 × Mills = Annual tax (1 mill = $1 per $1,000)Mills are thousandths; use assessed value, not market value.
14. Assessed value
Market value × Assessment ratio = Assessed valueThe assessment ratio connects what it would sell for to what it is taxed on.
15. Capitalization rate
I ÷ R = V · I ÷ V = R · R × V = II = NET operating income (never gross rent, never after debt service)IRV: cover the letter you want and the triangle gives you the operation.
16. Profit & loss %
(Sold − Paid) ÷ Paid = % profit(Paid − Sold) ÷ Paid = % lossAlways measured against what was paid, never the sale price.
17. Depreciation
Building value ÷ Useful life (years) = Annual depreciationStraight-line. Only the building depreciates — subtract land first.
18. Gross rent multiplier
Price ÷ Gross rent = GRMGROSS rent, no units; watch whether the rent is monthly or annual.
19. Owner equity
Market value − Mortgage balance = EquityCurrent value minus what is owed — not value minus the original price.
20. Finding the rate
Commission ÷ Sale price = Rate (Part ÷ Whole = Rate)The sale price is always the whole in a commission problem.
Sheet matches the free math drills; no calculator with an alphabetic keyboard is allowed on exam day.