Financial Calculations

Mortgage Loan Originators must master key financial calculations to accurately quote loan terms, prepare disclosures, and help borrowers understand their costs. This section covers the essential formulas and calculations tested on the SAFE MLO exam.

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1. Periodic Interest Calculations

Per Diem Interest Formula

Per diem (daily) interest is used to calculate interest charges for partial months, typically at closing when the loan funds mid-month.

Formula:

Per Diem Interest = (Loan Amount × Annual Interest Rate) ÷ 365

Step-by-Step Example

Given: $300,000 loan at 6.5% annual interest rate

Step 1: Convert the percentage to decimal

• 6.5% = 0.065

Step 2: Calculate annual interest

• $300,000 × 0.065 = $19,500 per year

Step 3: Divide by 365 days

• $19,500 ÷ 365 = $53.42 per day

Prepaid Interest Calculation

If a loan closes on January 15th, the borrower pays interest from January 15th through January 31st (17 days):

• 17 days × $53.42 = $908.14 prepaid interest at closing

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2. Monthly Payment Calculations (PITI)

PITI represents the total monthly housing payment:

• P = Principal
• I = Interest
• T = Taxes (property taxes in escrow)
• I = Insurance (homeowners insurance in escrow)

Principal & Interest (P&I) Formula

The monthly mortgage payment formula is:

M = P × [r(1+r)^n] / [(1+r)^n - 1]

Where:

• M = Monthly payment
• P = Principal (loan amount)
• r = Monthly interest rate (annual rate ÷ 12)
• n = Total number of payments (years × 12)

Step-by-Step PITI Example

Given:

• Loan Amount: $300,000
• Interest Rate: 6.5% (0.065 annual, 0.005417 monthly)
• Loan Term: 30 years (360 payments)
• Annual Property Taxes: $4,800
• Annual Homeowners Insurance: $1,800

Step 1: Calculate Principal & Interest (P&I)

• Using the formula or mortgage factor tables:
• P&I = $1,896.20 per month

Step 2: Add monthly property tax escrow

• $4,800 ÷ 12 = $400.00 per month

Step 3: Add monthly insurance escrow

• $1,800 ÷ 12 = $150.00 per month

Step 4: Calculate Total PITI

• $1,896.20 + $400.00 + $150.00 = $2,446.20 PITI

PITI for DTI Calculations

When calculating front-end DTI (housing ratio):

Front-End DTI = PITI ÷ Gross Monthly Income

Example: $2,446.20 PITI ÷ $8,000 gross income = 30.6% front-end DTI

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3. Down Payment Requirements by Loan Type

Different loan programs have different minimum down payment requirements:

Down Payment Calculation Examples

Conventional Loan (5% down):

• Home Price: $400,000
• Down Payment: $400,000 × 0.05 = $20,000
• Loan Amount: $400,000 - $20,000 = $380,000
• LTV: $380,000 ÷ $400,000 = 95% (PMI required)

FHA Loan (3.5% down):

• Home Price: $400,000
• Down Payment: $400,000 × 0.035 = $14,000
• Base Loan Amount: $400,000 - $14,000 = $386,000
• UFMIP (1.75%): $386,000 × 0.0175 = $6,755 (can be financed)
• Total Loan: $386,000 + $6,755 = $392,755

VA Loan (0% down):

• Home Price: $400,000
• Down Payment: $0
• Loan Amount: $400,000
• VA Funding Fee: 2.15% (first use) = $8,600 (can be financed)

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4. Closing Cost Estimates

Closing costs typically range from 2% to 5% of the loan amount. Understanding each component helps MLOs provide accurate Loan Estimates.

Common Closing Cost Components

Step-by-Step Closing Cost Example

Given: $300,000 loan amount

Step 1: Calculate percentage-based fees

• Origination Fee (1%): $300,000 × 0.01 = $3,000
• Discount Points (1 point): $300,000 × 0.01 = $3,000
• Title Insurance (0.5%): $300,000 × 0.005 = $1,500

Step 2: Add fixed fees

• Appraisal: $550
• Credit Report: $40
• Title Search: $300
• Recording Fees: $175
• Flood Cert: $20

Step 3: Calculate Total Closing Costs

• $3,000 + $3,000 + $1,500 + $550 + $40 + $300 + $175 + $20 = $8,585
• Percentage of loan: $8,585 ÷ $300,000 = 2.86%

Note: This does not include prepaid items (taxes, insurance, per diem interest) which are additional costs at closing.

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5. ARM Adjustment Calculations

Adjustable-Rate Mortgages (ARMs) have rates that change periodically based on an index plus a margin.

ARM Rate Formula

Fully Indexed Rate = Index + Margin

Key ARM Terms

Step-by-Step ARM Adjustment Example

Given:

• Initial Rate: 5.00% (Year 1)
• Index (SOFR): 4.50% at first adjustment
• Margin: 2.75%
• Periodic Cap: 2%
• Lifetime Cap: 5%

Step 1: Calculate the Fully Indexed Rate

• Index + Margin = 4.50% + 2.75% = 7.25%

Step 2: Apply the Periodic Cap

• Current Rate: 5.00%
• Maximum Increase: 5.00% + 2.00% = 7.00%
• Fully Indexed Rate: 7.25%
• New Rate: 7.00% (capped at 2% increase)

Step 3: Check Lifetime Cap

• Initial Rate: 5.00%
• Lifetime Cap: 5.00%
• Maximum Rate Ever: 5.00% + 5.00% = 10.00%
• Current adjusted rate (7.00%) is below lifetime cap ✓

ARM Adjustment Scenario Analysis

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Exam Tips for Financial Calculations

For the SAFE MLO Test, remember:

• Per diem interest: (Loan Amount × Rate) ÷ 365
• Prepaid interest: Days remaining in month × per diem amount
• PITI includes: Principal, Interest, Taxes, Insurance
• Down payment: Conventional 3-20%, FHA 3.5%, VA 0%, USDA 0%
• PMI required: When LTV exceeds 80% on conventional loans
• Closing costs: Typically 2-5% of loan amount
• 1 discount point = 1% of loan amount = typically reduces rate by 0.25%
• ARM fully indexed rate = Index + Margin
• Periodic caps limit each adjustment (usually 2%)
• Lifetime caps limit total increase (usually 5-6%)
• Tolerance limits apply to fees disclosed on Loan Estimate

Quick Reference: Financial Calculation Formulas