Loans: the anatomy of a payment

You finance a $40,000 truck at 7% for five years. The lender says $792 a month, and that number is honest — what it hides is the RECIPE inside each payment, which changes every single month you pay.

The level payment

Amortization means paying interest on the remaining balance PLUS enough principal that the loan dies exactly on schedule, with every payment the same size. The formula that balances all sixty payments:

$\text{PMT} = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$

with monthly rate r = 0.07 ÷ 12 and n = 60 payments:

$\text{PMT} = \$40{,}000 \times \frac{0.005833 \times 1.4176}{0.4176} \approx \$792 \text{ / month}$

The flip inside the payment

Month 1: the balance is $40,000, so interest is 40,000 × 0.005833 = $233, and only $559 of your $792 touches the principal. Month 60: the balance is nearly gone, interest is pocket change, and almost the whole payment is principal. Year by year:

Early payments are the lender's; late payments are yours. Two practical consequences fall straight out of the picture:

• Extra principal is most powerful EARLY. An extra $100 in year 1 kills balance that would have billed 7% for four more years.
• Payoff quotes surprise people. After 2 of 5 years you've paid $19,010 — but the balance is still $25,652, because $4,662 of those payments were interest, not truck.

Total cost: 60 × $792 = $47,524. The 7% truck cost $7,524 to finance — about 19% of its price.

Don't confuse the loan with the depreciation

Lesson 2 charged $400/month of equipment depreciation to overhead. This lesson computed a $792/month loan payment. They are different answers to different questions: depreciation spreads the truck's COST over its useful life (what owning it consumes); the payment is CASH leaving on a schedule (how you financed it). Your overhead rate carries the depreciation and the interest — not the principal, which is just moving money from one pocket to the lender's ledger of a truck you now own more of.

One question remains for the module: if money grows forward along the curve, what is money that arrives LATER worth NOW? That's present value — the last tool, next.