Chapter 4 — Key Takeaways
The formulas
| Quantity | Formula |
|---|---|
| Monthly P&I | $M = P \cdot \dfrac{i}{1-(1+i)^{-n}}$ — $i$ is monthly, $n$ is months |
| One month's interest | balance × (annual rate ÷ 12) |
| Amortization, one line | interest = balance × monthly rate · principal = payment − interest · new balance = old − principal |
| PITI | P&I + taxes/12 + insurance/12 + MI + HOA |
| LTV | loan ÷ lesser of price or appraised value |
| CLTV / HCLTV | all liens ÷ value · HCLTV uses the full HELOC line |
| Housing ratio | PITI ÷ gross monthly income |
| Back-end (DTI) | (PITI + other monthly debts) ÷ gross monthly income |
| Discount point | 1% of the loan amount |
| Points break-even | cost of points ÷ monthly payment saved (in months) |
| Amount financed | loan amount − prepaid finance charges |
| Per-diem interest | loan amount × annual rate ÷ 365 |
| Payment shock | proposed PITI ÷ current housing cost |
The Linden Street file, fully derived
| Loan | \$385,000 × 95% = **\$365,750.00 · LTV 95.00%** |
| Monthly rate | 0.06625 ÷ 12 = 0.0055208333 |
| P&I | \$2,019.24 ÷ 0.862211 = **\$2,341.94** |
| First payment split | interest \$2,019.24** / principal **\$322.70 (13.8%) |
| PITI + MI | 2,341.94 + 385.00 + 130.00 + 176.78 = \$3,033.72 |
| Housing ratio | 3,033.72 ÷ 10,500.00 = 28.89% |
| Back-end (DTI) | 4,479.72 ÷ 10,500.00 = 42.66% |
| Payment shock | 3,033.72 ÷ 1,850.00 = 1.64× (+64.0%) |
| Prepaid finance charges | \$6,095.34 |
| Amount financed | \$359,654.66 |
| APR | 7.253% — 0.628 pts above the note rate, mostly MI |
| Per-diem interest | \$66.3861/day** · 8 days = **\$531.09 |
| Total of 360 payments | \$843,098.40** · total interest **\$477,348.40 (1.31×) |
| MI cancellation | request at payment 125 (80%) · automatic at 137 (78%) |
The rules that decide files
- LTV uses the lesser of price or appraised value. This is why a low appraisal is a cash problem and not a debate.
- 80% = request, 78% = automatic, both against original value, both under the Homeowners Protection Act, both for conventional borrower-paid PMI only. FHA MIP follows different rules.
- A point is 1% of the loan amount, not the price.
- Dollars are canonical. Never back-compute a dollar figure from a rounded percentage.
What DTI cannot measure
Taxes (it uses gross income) · household size and childcare · non-debt expenses like medical care, tuition, or a long commute · the difference between a student loan and a boat payment · the direction a household is heading.
And it declines borrowers who have already proven the behavior — someone paying \$2,800 rent on time for six years, failing on a \$2,400 PITI because of student debt.
Payment shock is the number nobody computes and everybody lives with.
The rules of thumb
- Quote PITI, always, and say the letters out loud. Never quote bare P&I.
- Never quote a rate without four facts: representative score, LTV, occupancy and property type, lock period.
- Mental estimate: payment per \$1,000 at 30 years — \$5.37 at 5%, \$6.00 at 6%, **\$6.40 at 6.625%**, \$6.65 at 7%, \$7.34 at 8%. Multiply by the loan in thousands.
- Sanity check: the real payment is above interest-only by about 29% at 5%, 16% at 6.625%, 10% at 8%. Lower rate, wider gap.
- Show the division, not the percentage. Borrowers who see the arithmetic trust the result.
- Give every number its uncertainty. Say which figures are firm, close, and genuinely soft.
Key terms
principal · interest · amortization · amortization schedule · PITI · LTV · CLTV · HCLTV · housing ratio · back-end ratio / DTI · ten-month rule · payment shock · discount point · origination charge · par rate · lender credit · break-even · APR · amount financed · finance charge · prepaid finance charge · per-diem interest · prepaid interest · negative amortization
Monday morning
You should be able to:
- Produce a PITI estimate on the phone in ninety seconds, with a stated range and basis
- Compute both ratios in front of a borrower and show the division
- Tell a borrower instantly what a \$13,000 low appraisal costs them in cash
- Explain the APR gap in under 80 words and hand them a way to use it while shopping
- Compute a points break-even and name the one question that decides it
- Compute payment shock — and raise it even though nobody asked
The one sentence
DTI answers the underwriter's question. Payment shock answers the borrower's. You are the only person in the transaction who will ask the second one.