Est. 2026 · Empire City Financial

The Time Value Of Money

A dollar tonight beats a dollar tomorrow. This city runs on it.

▼ DOWNTOWN · TVM CONSOLE ▼

The big idea

A dollar today is worth more than a dollar next year, because today's dollar can start earning interest right now. Every loan, savings plan, and retirement account is just this one idea wearing a different coat.

How the console works

Every money plan has five dials: TIME how long it runs, RATE what it earns or costs per year, TODAY what's on the table now, CONTRIBUTION the cash you add on repeat — monthly or weekly, and THE END where it all lands. Feed the console today, and it projects THE END — or flip the question and solve any dial from the other four.

The one rule

Direction matters, and it's simple: money you put in is positive. Investing $10,000 today? 10000. Contributing $500 a month? 500. The one flip: money handed to you — like a loan — goes in as negative.

TVM CONSOLE

Step 1 · What you put in

What you invest today. Handed money instead — like a loan? Make it negative.

Optional — blank or 0 means none. 500 means $500 in, every time.

Contribute ·

Step 2 · Set the return — and how long

Yearly rate. Savings run about 4; markets about 7.

How many years you let it ride. 2.5 works too.

Step 3 · The projection

READY
— — —

Dial in where you stand today, then project where you land.

The one rule: money you put in is positive; money handed to you (a loan) is negative.

Balance over time appears here after a run.

Flip the question · Solve for something else

Where the balance lands when time's up.

Or · Load a ready-made mission

Each mission loads a real scenario into the dials above and runs it.

Under the hood · The math

PV·(1+i)ᴺ + PMT·(1+i·τ)·[((1+i)ᴺ−1)/i] + FV = 0
τ = 1 when payments land at the beginning of each period · 0 when they land at the end

One equation runs this whole console: what's on the table today, grown by interest, plus every payment along the way, grown by interest, plus whatever's left at the end — it all has to sum to zero. You type years and a yearly rate; the console quietly converts to months (years × 12) and a monthly rate (rate ÷ 12) before solving.