Real Estate Math – Florida Salesperson Exam Prep

Complete Study Guide

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Overview

This study guide covers the essential math concepts tested on the Florida Real Estate Salesperson Exam, including commission calculations, property valuation, mortgage financing, proration, land measurement, and investment analysis. Mastery of these calculations requires understanding the underlying formulas, knowing when to apply each method, and practicing the part/rate/total relationship that underpins nearly every problem. Consistent formula application and careful attention to what the question is actually asking are the keys to exam success.

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The Foundation: Part ÷ Rate = Total

Before diving into categories, internalize this universal formula:

```

Part ÷ Rate = Total

Part ÷ Total = Rate

Total × Rate = Part

```

> Almost every real estate math problem is a variation of this triangle. Identify which two values you have, and solve for the third.

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Section 1: Commission Calculations

Overview

Commission problems test your ability to work through multi-step splits and to work backward from a known result to find an unknown (sale price or rate).

Core Formulas

| Goal | Formula |

|---|---|

| Total Commission | Sale Price × Commission Rate |

| Broker's Share | Total Commission × Broker's % |

| Salesperson's Share | Broker's Share × Salesperson's % |

| Sale Price from Commission | Commission Earned ÷ Commission Rate |

| Net Sale Price (seller's net) | Net ÷ (1 – Commission Rate) |

Step-by-Step Process for Split Commissions

1. Calculate total commission (Sale Price × Rate)

2. Determine each broker's share (Total × their %)

3. Determine salesperson's cut (Broker's share × salesperson's %)

Key Concepts

Worked Examples

Tiered Commission:

Seller's Net Problem:

Reverse-Engineer Sale Price:

Key Terms

Watch Out For

> ⚠️ Multi-step splits: Don't forget there are often TWO splits — the broker-to-broker split AND the broker-to-salesperson split. Work through each step sequentially.

> ⚠️ Seller's net problems: Never subtract the commission rate from the sale price. Always divide by `(1 – rate)`. A common error is multiplying the net by `(1 + rate)`.

> ⚠️ Tiered commissions: Apply each rate only to its designated price range, not the full sale price.

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Section 2: Property Valuation & Appraisal Math

Overview

Appraisal math covers three approaches to value (income, cost, and sales comparison), property tax calculations, and depreciation.

The Three Approaches to Value

#### Income Approach (Capitalization)

```

Value = NOI ÷ Cap Rate

Cap Rate = NOI ÷ Value

NOI = Value × Cap Rate

```

| Known | Unknown | Formula |

|---|---|---|

| NOI + Cap Rate | Value | NOI ÷ Cap Rate |

| NOI + Value | Cap Rate | NOI ÷ Value |

| Value + Cap Rate | NOI | Value × Cap Rate |

#### Cost Approach

```

Value = (Replacement Cost – Accumulated Depreciation) + Land Value

```

#### Sales Comparison Approach (Adjustments)

```

Adjusted Comp Value = Comp Sale Price – Features Comp Has (that subject lacks) + Features Subject Has (that comp lacks)

```

Remember the rule: Adjust the comparable, not the subject property.

Property Tax Calculations

```

Assessed Value = Market Value × Assessment Ratio

Annual Tax = Assessed Value × Mill Rate

Mill Rate Conversion: mills ÷ 1,000 (e.g., 15 mills = 0.015)

```

Example:

Key Terms

Watch Out For

> ⚠️ Sales comparison adjustments: Students frequently add when they should subtract and vice versa. Always ask: "Am I adjusting the comp to make it equal to the subject?" If the comp is better, subtract value.

> ⚠️ Mill rate conversion: Always divide mills by 1,000 before multiplying. 22 mills = 0.022, NOT 0.22.

> ⚠️ Land in cost approach: Never depreciate land. Only depreciate the building/improvements.

> ⚠️ Cap rate direction: A higher cap rate means a lower value. This is counterintuitive to many students.

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Section 3: Mortgage & Financing Math

Overview

Mortgage math covers loan amounts, down payments, interest calculations, loan costs (points), PMI, and qualifying ratios.

Core Formulas

| Concept | Formula |

|---|---|

| Loan Amount | Purchase Price × LTV% |

| Down Payment | Purchase Price × (1 – LTV%) |

| Monthly Interest | Principal × (Annual Rate ÷ 12) |

| Discount/Origination Points | Loan Amount × (Points% ÷ 100) |

| Annual PMI | Loan Amount × PMI Rate |

| Monthly PMI | Annual PMI ÷ 12 |

| Front-End DTI | Monthly Housing Payment ÷ Gross Monthly Income |

| Maximum P&I | Total PITI – Taxes – Insurance |

Key Concepts Explained

Loan-to-Value (LTV):

Discount Points:

PITI:

Private Mortgage Insurance (PMI):

Debt-to-Income (DTI):

Key Terms

Watch Out For

> ⚠️ Points are based on the loan amount, not the purchase price. If the purchase price is $300,000 and the LTV is 90%, the loan is $270,000 — calculate points on $270,000.

> ⚠️ Monthly interest calculation: Divide the annual rate by 12 first, then multiply by the balance. Do NOT divide the annual payment by 12.

> ⚠️ PMI threshold: PMI is based on the loan balance, not purchase price. Recalculate the loan amount first.

> ⚠️ DTI vs. P&I: The exam may give you PITI and ask for P&I, or vice versa. Read carefully.

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Section 4: Proration Calculations

Overview

Proration allocates expenses and income between buyer and seller at closing based on who owns the property and for how long.

Two Calendar Methods

| Method | Year | Month |

|---|---|---|

| Banker's (360-day) | 360 days | 30 days |

| Actual (365-day) | 365 days | Actual days |

> Florida default: The 365-day (actual days) method, unless the contract specifies otherwise.

Proration Process

Step 1: Calculate the daily rate

Step 2: Count the number of days for seller's or buyer's portion

Step 3: Multiply daily rate × number of days

Step 4: Determine who pays whom (credit/debit)

Who Gets the Credit?

| Item | Paid in Advance (prepaid) | Paid in Arrears (unpaid) |

|---|---|---|

| Property taxes | Buyer owes seller (seller paid more than their share) | Seller owes buyer (seller used time without paying) |

| Rent collected | Buyer receives credit (buyer owns the days) | N/A |

| Insurance (assumed) | Buyer owes seller (buyer inherits unused coverage) | N/A |

Closing Day Rule

> In Florida, the seller owns the property on the day of closing. The buyer's proration period begins the day after closing.

Key Worked Example

Annual taxes of $3,600; closing March 1; seller hasn't paid (360-day method)

Key Terms

Watch Out For

> ⚠️ Which method to use: The exam will specify 360 or 365. Don't assume — read the question.

> ⚠️ Who gets the credit: Taxes paid in arrears → seller owes buyer. Taxes prepaid → buyer owes seller. Think about who used what period.

> ⚠️ Rent proration: Rent is typically paid in advance. The buyer gets credit for the days they own the property during the prepaid period.

> ⚠️ Closing day ownership: Seller owns closing day; buyer's period starts the next day.

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Section 5: Area & Land Calculations

Overview

Land math involves converting between measurement units, calculating areas of various shapes, and applying the rectangular survey system.

Essential Conversions & Facts

| Unit | Equivalent |

|---|---|

| 1 acre | 43,560 square feet |

| 1 section | 640 acres = 1 square mile |

| 1 township | 36 sections (6 miles × 6 miles) |

| 1 mile | 5,280 feet |

Rectangular Survey System — Subdividing Sections

```

Full Section = 640 acres

½ Section = 320 acres

¼ Section = 160 acres

¼ of ¼ Section = 40 acres

```

Formula: 640 ÷ (denominator × denominator for each fraction)

Example: NW¼ of SW¼ = 640 × (1/4) × (1/4) = 40 acres = 40 × 43,560 = 1,742,400 sq ft

Area Formulas

| Shape | Formula |

|---|---|

| Rectangle/Square | Length × Width |

| Triangle | ½ × Base × Height |

| Trapezoid | ½ × (Base₁ + Base₂) × Height |

| Circle | π × radius² |

Converting Area to Acres

```

Acres = Square Feet ÷ 43,560

```

Price Per Square Foot

```

Total Price = Area (sq ft) × Price per sq ft

Price per sq ft = Total Price ÷ Area

```

Key Terms

Watch Out For

> ⚠️ Memorize 43,560: This number is critical. You will need it to convert square feet to acres.

> ⚠️ Section fractions multiply: NW¼ of SW¼ is NOT ¼ + ¼. It is ¼ × ¼ = 1/16 of a section.

> ⚠️ Triangle area: Don't forget the ½ factor. Many students calculate base × height and forget to halve it.

> ⚠️ Units consistency: Make sure length and width are in the same units before calculating.

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Section 6: Investment & Return Calculations

Overview

Investment math evaluates the profitability of income-producing properties using NOI, cap rates, GRM, and cash-on-cash returns.

Core Investment Formulas

| Concept | Formula |

|---|---|

| NOI | Effective Gross Income – Operating Expenses |

| Effective Gross Income | Gross Rents × (1 – Vacancy Rate) |

| Value (Cap Rate method) | NOI ÷ Cap Rate |

| Required NOI | Investment Value × Required Return |

| Value (GRM method) | Monthly Gross Rent × GRM |

| Simple ROI | (Profit ÷ Original Investment) × 100 |

| Cash-on-Cash Return | Annual Cash Flow ÷ Cash Invested (down payment) |

| Annual Cash Flow | NOI – Annual Mortgage Payments (debt service) |

NOI Calculation — Step by Step

1. Start with Potential Gross Income (PGI) — total rent if 100% occupied

2. Subtract vacancy and credit losses →