# Worked Example — Loan Decoder

## The brief

Sam is buying a used car and the dealership's financing desk slides over an offer: $24,000 loan, 72 months, "only $429/month, 5.9% rate." A credit-union pre-approval in Sam's inbox says 6.4% for 60 months. "The dealer's is lower — just sign here, right?"

## The output

### Loan Decode: dealership financing vs credit-union pre-approval

**The verdict:** The dealer's "lower rate" costs **$1,509 more** than the credit union's higher one. The advertised 5.9% hides a longer term, a doc fee financed into the principal, and a prepayment catch. Numbers first, then the trap-by-trap.

**Total-cost-of-loan — the only number that matters**

| | Dealer offer | Credit union |
|---|---|---|
| Amount financed | $24,000 **+ $900 fees** = $24,900 | $24,000 |
| Rate (APR) | 5.9% *quoted* → **6.55% effective APR** with fees | 6.4% |
| Term | 72 months | 60 months |
| Monthly payment | $429 | $469 |
| **Total paid** | **$30,888** | **$28,140** |
| **Total interest + fees** | **$6,888** | **$4,140** |

**The traps, decoded**
1. **Rate vs APR** — 5.9% is the *note rate*; financing the $900 "documentation and processing" fee makes the effective APR ~6.55%. The advertised number excludes exactly what the law's APR figure exists to include. Ask: *"What is the APR including all financed fees?"*
2. **The term stretch** — 72 vs 60 months is why the payment looks friendlier. Twelve extra months of interest is where the $1,509 hides. A lower payment is not a cheaper loan.
3. **Prepayment language** — §6: "interest computed by the Rule of 78s in the first 24 months." That front-loads interest so early payoff saves less than expected. The credit union's simple-interest note has no such clause. Ask: *"Is interest simple, and is there any prepayment penalty or Rule of 78s?"*
4. **The add-on layer** — GAP insurance ($795) and a "protection package" ($1,200) appear pre-checked on the worksheet. Both are declinable; GAP from your own insurer typically runs ~$300.

**The three questions that most change the deal**
1. "What's the total amount I will have paid after the last payment?" (forces the $30,888 into the open)
2. "APR with all fees financed, and is it simple interest?"
3. "Will you beat $28,140 total on a 60-month term?" — dealers can often re-quote when the comparison is total-cost.

**Decision:** take the credit-union loan unless the dealer beats **$28,140 total**, simple interest, no financed fees. The payment being $40 higher for 12 fewer months is the cheaper deal wearing the scarier shirt.

*This is a plain-language reading, not financial advice — terms vary by lender and state; confirm anything load-bearing with a qualified professional.*

## Why it's shaped this way

- **Total-paid leads the table** — the skill's core rule: the loan with the smaller monthly and the bigger total is the trap the monthly-payment frame exists to sell.
- **The APR reconciliation is computed, not asserted** — 5.9% → 6.55% with the financed fee shown; that arithmetic is the decode.
- **Rule of 78s is quoted and explained in one sentence** — obscure clause, concrete consequence, per the fine-print mandate.
- **Pre-checked add-ons get their market comparison** ($795 vs ~$300) — a flag with a number beats "watch out for add-ons."
- **The decision line names the exact beat-this number** — decoders end in leverage: a figure to put on the desk.
- **The disclaimer appears verbatim**, as every decoder requires.