A real estate math problem often goes wrong before anyone touches a calculator. The percentage is applied to the wrong amount, a millage rate is read as a percent, or an annual charge is divided by the wrong number of days.
Start by writing three things: what you know, what the question asks for, and the unit your answer should use. Dollars, days, and percentages are not interchangeable.
Loan-to-value: keep the two amounts straight
$234,000
Loan amount in this hypothetical exercise.
$300,000
Property value used by the exercise.
78% LTV
$234,000 divided by $300,000, then multiplied by 100.
The figures below are invented for practice. They are not actual transaction results, typical commissions, mortgage offers, or local tax rates. These are original study questions, not questions taken from the state examination.
1. Commission: use the amount the split actually applies to
The problem: A brokerage earns a negotiated fee equal to 2.5% of a $360,000 sale price. Under the hypothetical associate agreement, the associate receives 60% of that brokerage fee. What is the associate's share before other deductions?
There are two calculations, with two different starting amounts:
- Brokerage fee: $360,000 × 0.025 = $9,000.
- Associate's share: $9,000 × 0.60 = $5,400.
The mistake to avoid: multiplying the sale price directly by 60%. The associate's percentage applies to the brokerage fee in this example, not to the value of the property.
Check the size of the answer. A 60% share should be more than half of $9,000 but less than the full amount. $5,400 fits. It is a share before deductions, not take-home income after taxes or business expenses.
No rate in this example is a standard or required charge. The National Association of Realtors' listing-agreement guide explains that compensation is negotiated rather than fixed by law.
2. Loan-to-value: put the loan on top
The problem: A loan is $234,000 and the property value specified in the question is $300,000. What is the loan-to-value ratio?
LTV = loan amount ÷ property value × 100
$234,000 ÷ $300,000 = 0.78, so the answer is 78%.
The Consumer Financial Protection Bureau's LTV explanation compares financing with the property's appraised value. For a practice problem, identify the value the question tells you to use. Do not silently replace it with a different number mentioned elsewhere.
The mistake to avoid: reversing the fraction. Dividing $300,000 by $234,000 answers a different question.
As a quick check, a loan smaller than the stated property value should produce an LTV below 100%. This calculation does not tell you whether a lender would approve the loan, what its interest rate would be, or which other lending conditions apply.
3. Millage: divide by 1,000, not by 100
The problem: A property's taxable value is $250,000. For this simplified exercise, an aggregate rate of 18.2 mills applies to that same taxable value. What is the resulting ad valorem tax amount?
Taxable value ÷ 1,000 × millage = tax
$250,000 ÷ 1,000 = 250. Then 250 × 18.2 = $4,550.
A mill is one dollar per $1,000 of taxable value. Another way to enter the same calculation is $250,000 × 0.0182. The Florida Department of Revenue's property-tax explanation distinguishes just, assessed, and taxable values and shows how exemptions affect the calculation.
The mistake to avoid: treating 18.2 mills as an 18.2% rate, or substituting a listing price for the taxable value given in the question.
Real tax bills can involve different taxable bases for different taxing authorities and additional assessments. The exercise deliberately supplies one common taxable value and excludes other charges. It is not an estimate of a buyer's future tax bill.
4. Proration: use the day-count convention you are given
The problem: A practice settlement question allocates a $3,600 annual charge between two parties. It expressly requires a 360-day year and assigns 90 days to the seller. What amount is allocated to the seller?
- Daily amount: $3,600 ÷ 360 = $10.
- Seller's allocation: $10 × 90 = $900.
The mistake to avoid: using 365 because that is the number you remember from another problem. Here, 360 is an explicit assumption. A different question may specify a different convention.
The problem gives you the seller's day count, so you do not need to decide who owns the closing day. It also asks only for the allocation, not a debit or credit. To identify those entries, you would need more facts, including whether the charge has already been paid. In a real transaction, use the applicable contract and settlement instructions, not this classroom example.
Try changing the numbers
Cover the worked answers and solve these variations:
- The brokerage fee is $8,000 and the associate's stated share is 55%. What is the share?
- The loan is $216,000 against a stated property value of $270,000. What is the LTV?
- A single taxable base of $180,000 is subject to 16.5 mills. What tax amount results?
- A $2,880 annual charge uses a 360-day year, with 75 days allocated to one party. What is that allocation?
Answers: $4,400; 80%; $2,970; and $600. If one differs from your result, check the starting amount and units before changing the arithmetic.
For more practice, visit the real estate computations questions or explore the 63Hours course introduction. Aim to explain why the formula fits the question. That skill is more useful than remembering the last answer you clicked.