Money now vs money later

Would you rather have $9,500 today or $10,000 in a year? Gut answers split the room. Present value ends the argument: it converts money at ANY future date into today's dollars, so every offer stands on the same line and the bigger number simply wins.

Compounding, run backward

If money grows forward by (1 + r)ᵗ, then future money shrinks back by the same factor:

$\text{PV} = \frac{\text{FV}}{(1+r)^t}$

The r here is YOUR discount rate — what money is worth per year in your hands. Use what waiting actually costs you: the rate your credit line charges, or the return idle cash earns. Say 6%:

$\text{PV of } \$10{,}000 \text{ in 1 year} = \frac{\$10{,}000}{1.06} = \$9{,}434$

So the choice was never close: $9,500 today beats $10,000 next year by $66 — at 6%. At a 10% discount rate (money is expensive for you), the future offer is worth only $9,091 and today wins by more. The answer depends on r, and that's not a bug: it's the honest admission that time is worth different amounts to different businesses.

Reading the shrink

Each year of waiting at 6% shaves the bar again — five years out, $10,000 is worth $7,473 today. Three places this one move earns its keep:

• Pay-now discounts. A supplier offers 2% off for paying now instead of in 30 days. Trivial? That's 2% for one month — over 26% a year. If your money costs less than that, take every one of these you see.
• Installment offers. "$5,200 now or $1,000/quarter for 6 quarters": discount each $1,000 back and compare the SUM of PVs against $5,200 — one line, no debate.
• Equipment decisions. A machine promising $3,000/year of savings for 5 years is NOT worth $15,000 today — at 6% the discounted stream is about $12,637. Compare prices against that number.

The module in one sentence

Compound interest grows money forward; amortization schedules the cost of borrowing it; present value drags every future dollar back to today so decisions compare fairly. One capstone remains: assembling everything — costs, overhead, margin, terms, time — into a single estimate that deserves to be signed.