lending

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---
name: lending
description: "Analyze lending products including mortgages, HELOCs, and personal loans with amortization and comparison tools. Use when the user asks about mortgage comparison, fixed vs ARM rates, loan qualification, amortization schedules, extra payments, or buying points. Also trigger when users mention 'monthly payment calculation', '15-year vs 30-year mortgage', 'PMI', 'APR vs interest rate', 'HELOC', 'home equity', 'should I buy down the rate', 'biweekly payments', or ask how much house they can afford."
---

# Lending Analysis

## Core Concepts

### Fixed-Rate Mortgage
The interest rate and monthly payment remain constant for the life of the loan:

- **Advantages:** Predictable payments, protection against rising rates, simpler budgeting
- **Disadvantages:** Higher initial rate than ARM, no benefit if rates decline (must refinance)
- Most common terms: 30-year and 15-year fixed

### Adjustable-Rate Mortgage (ARM)
Rate is fixed for an initial period, then adjusts periodically based on an index plus a margin:

- **Notation:** 5/1 ARM = fixed for 5 years, adjusts annually thereafter; 7/1, 10/1 similarly
- **Fully indexed rate:** Index (e.g., SOFR, 1-year Treasury) + margin (e.g., 2.75%)
- **Rate caps** protect against extreme adjustments:
  - Initial adjustment cap (e.g., 2%): maximum first adjustment
  - Periodic cap (e.g., 2%): maximum change per adjustment period
  - Lifetime cap (e.g., 5%): maximum total increase over initial rate
- **When ARM may be appropriate:** Planning to sell or refinance before the fixed period ends, expecting rates to decline, or comfortable with rate variability

### Monthly Payment Calculation
The standard amortization formula for a fixed-rate loan:

- PMT = P × [r(1+r)^n] / [(1+r)^n - 1]
- Where: P = principal (loan amount), r = monthly interest rate (annual rate / 12), n = total number of payments (term in months)
- Each payment splits into interest (decreasing) and principal (increasing) components:
  - Interest portion: remaining balance × monthly rate
  - Principal portion: PMT - interest portion

### Total Interest Paid
- Total interest = (n × PMT) - P
- For a $400K, 30-year loan at 6.5%: PMT = $2,528, total payments = $910,178, total interest = $510,178

### Extra Payments
Additional principal payments reduce the outstanding balance, shorten the loan term, and reduce total interest:

- Each extra dollar goes entirely to principal reduction
- Impact compounds: earlier extra payments save more interest than later ones
- Methods: lump sum, fixed monthly extra, biweekly payments (26 half-payments = 13 full payments per year)

### Mortgage Points
Prepaid interest that reduces the loan's interest rate:

- **1 point = 1% of the loan amount** (e.g., 1 point on $400K = $4,000)
- Typically reduces the rate by approximately 0.25% (varies by lender and market)
- **Breakeven calculation:** Points cost / monthly savings = months to recoup
- Points make sense when: planning to hold the loan beyond breakeven, itemizing deductions (points may be tax-deductible in year of purchase)

### APR vs Interest Rate
- **Interest rate:** The cost of borrowing the principal, expressed annually
- **APR (Annual Percentage Rate):** Includes the interest rate plus certain fees and costs (origination fees, points, PMI), annualized over the loan term
- **APR > interest rate** (always, when there are fees)
- APR is the better metric for comparing loan offers with different fee structures

### HELOC (Home Equity Line of Credit)
A revolving credit line secured by home equity:

- **Combined LTV (CLTV):** (First mortgage balance + HELOC limit) / home value
  - Most lenders require CLTV ≤ 80-90%
- **Draw period** (typically 10 years): borrow and repay flexibly, often interest-only payments
- **Repayment period** (typically 20 years): no new draws, fully amortizing payments
- **Variable rate:** Typically prime rate + margin; rate fluctuates with market
- **Use cases:** Home improvements, debt consolidation, em