Equity Engine

🎯 The Math of Speed: Shorter payoff windows reduce the lender's amortization runway, unlocking hundreds of thousands of dollars in interest savings.

EQUITY ENGINE SLIDES SLIDE 5 OF 6

Loan Recasting vs. Refinancing

Advanced Tactics

TACTIC A

Loan Recasting

• • Client makes a large principal lump sum payment
• • Lender re-amortizes the remaining balance
• • Interest rate and remaining term do not change
• • Result: Lowers the mandatory monthly payment

TACTIC B

Refinancing

• • Borrower applies for a completely new mortgage loan
• • Replaces the existing loan with brand new parameters
• • Changes the interest rate, term length, and loan type
• • Result: incurs high closing costs and restarts term

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• Calculated LTV (%): \( \frac{\$425,000}{\$500,000} \times 100 = 85.0\% \)

• PMI Required? Yes. PMI is universally required on conventional financing when the calculated LTV exceeds 80.0% (meaning the borrower's down payment is less than 20%).

Problem 2: Debt-to-Income (DTI) Ratios

• Front-End DTI Calculation: Includes gross housing expenses (PITI). \[ \text{Front-End DTI} = \frac{\text{Monthly P\&I} + \text{Taxes \& Insurance}}{\text{Gross Income}} = \frac{\$2,686.20 + \$550.00}{\$10,200.00} = \frac{\$3,236.20}{\$10,200.00} \approx 31.73\% \]

• Back-End DTI Calculation: Includes housing expenses plus all other recurring obligations. \[ \text{Back-End DTI} = \frac{\$3,236.20 + \$650.00}{\$10,200.00} = \frac{\$3,886.20}{\$10,200.00} \approx 38.10\% \]

Part 2 Answer Key: Amortization Lab Solutions

Mathematical Justification: Interest Reduction Mechanics

Interest is computed directly on the outstanding principal balance: \( I_n = B_{n-1} \times \frac{r}{12} \). As monthly payments reduce \( B_{n-1} \), the product \( I_n \) must shrink. Because the scheduled monthly payment \( M \) remains constant, the principal portion \( P_n = M - I_n \) is algebraically forced to expand with each passing month.

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Teacher-Facing Dossier

EQUITY ENGINE SOLUTIONS

Answer Keys P3 & Exit Ticket

Part 3 Answer Key: Strategic Debt Acceleration

Problem 5: Advisory Strategy Comparison

• Mathematical Efficiency: Adding $300 monthly is highly efficient, saving $154,920.00 and cutting 7 years. Bi-weekly saves $102,712.00 and cuts 5.7 years.

• Implementation Risk: The bi-weekly strategy has low behavioral friction because half-payments sync perfectly with paycheck cycles. Adding $300 monthly is manual and vulnerable to budgeting changes or consumption temptations.

Problem 6: Recasting vs. Non-Modified Amortization

• Recasting: The lender recalculates monthly payments based on the new, smaller balance. The monthly payment falls, providing liquid flexibility, but the final loan maturity date is unchanged.

• Non-Modified Acceleration: The monthly payment remains at the original level. The loan matures years early because the principal paydown permanently eliminates the loan's tail end.

Exit Ticket Answer Key: Conceptual Audit

Question 1: DTI Calculation

Total monthly debt = \( \$2,100 \text{ (proposed housing)} + \$600 \text{ (other liabilities)} = \$2,700 \). Gross monthly income = \( \$8,000 \). \[ \text{Back-End DTI} = \frac{\$2,700}{\$8,000} = 33.75\% \] Qualification Status: Pass. The ratio of 33.75% is less than the strict 36% conventional benchmark limit.

Question 2: 300th vs 12th Payment Mechanics

By the 300th payment, the outstanding balance is dramatically lower. Interest is calculated as a direct percentage of the outstanding balance. With less interest accumulating, the fixed monthly payment is freed to pay off a much larger chunk of the outstanding principal balance.

Question 3: Bi-Weekly Acceleration Math

Making bi-weekly payments results in 26 half-payments, which translates directly to 13 full payments per year (one extra month's worth). Applying this entire extra payment directly to principal reduces the loan balance early, preventing a massive amount of future interest compounding.

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