decisions

Compound interest grows a dollar forward in time; present value runs the same machine in reverse, pulling a future dollar back to what it's worth today. The reason it's worth less is opportunity cost: a dollar you have now can be invested and grow, so a dollar you'll only receive in ten years has to be discounted to compare fairly. That single idea decides the most common 'big money' choice people actually face — lump sum or payments? A lottery that advertises an $800,000 jackpot may pay it as $40,000 a year for 20 years, and that stream is worth far less than $800,000 today because the distant payments are heavily discounted. Whether the cash option beats the payments depends entirely on your discount rate — the return you could earn on money in the meantime. This lesson builds the payment stream year by year: a dashed line climbs to the full face value (the headline), a solid line climbs only to the present value (what it's really worth), and a flat line marks the cash on the table. The key number the simulator surfaces is the break-even rate: the discount rate at which the stream and the lump are worth exactly the same, which is the implied return the payments 'pay' on the cash you'd give up. If you can reliably beat that rate, take the cash and invest it; if you can't, the guaranteed stream is worth more. The durable lessons: a headline total is not a present value; the discount rate is the master lever; and 'cash now versus payments later' is always really a question about what return you can earn.

A raise can never lower your take-home pay — that's the reassuring truth of the tax-bracket lesson, because only the new dollars are taxed at the higher rate. But take-home isn't the whole picture. A working family's net resources are take-home pay PLUS the means-tested benefits they qualify for: Medicaid or CHIP, an ACA premium subsidy, childcare assistance, SNAP, and refundable credits like the Earned Income Tax Credit. Many of those benefits are tied to an income limit, and some cut off all at once at a hard line — a 'cliff.' Cross it by a single dollar and the whole benefit vanishes, so a modest raise can leave a family with thousands less than before. The chart plots net resources against gross income: normally the line climbs, but at a cliff it drops, opening a 'trap zone' of incomes where earning more leaves you worse off, until your pay finally climbs back over the lost benefit. The number that exposes the myth is the effective marginal rate on a raise — and at a cliff it rockets past 100%, meaning the raise takes more than it gives. The opposite extreme also shows up: deep in the EITC phase-in, a raise is effectively subsidized, an effective rate below zero. The durable lessons: judge a money decision on net resources, not just salary; the most dangerous phase-outs are the abrupt ones; and the fix is almost never to turn down a raise — it's to leap well past the cliff, and for policy to taper benefits gradually instead of cutting them at a line.

Most people with a federal student loan never realize they chose a repayment plan — they took the default. But the choice between the standard 10-year plan and an income-driven plan (IDR) can swing the total cost by tens of thousands of dollars, in either direction. The standard plan is a fixed amortizing payment that clears the loan in 10 years: the highest monthly bill, the least interest, and debt-free fastest. An income-driven plan instead caps your payment at a share (often 10%) of your discretionary income — the part above roughly 150% of the poverty line — and forgives whatever balance is left after 20 or 25 years (10 years for public-service workers under PSLF). That lower payment is real relief when money is tight, but it hides a trap: when the payment is smaller than the month's interest, the unpaid interest is added to the balance and the loan GROWS — 'negative amortization.' So for a moderate earner, IDR can mean paying more in total, over twice as long, even after some forgiveness — the lower payment was just a longer, costlier loan. For a low earner whose income genuinely can't support the standard payment, the same plan is a lifeline: a tiny or zero payment, and a large balance wiped clean. The simulator races both balances over time so you can see the standard plan dive to zero while the income-driven balance climbs above what you borrowed before forgiveness erases the rest. The durable lessons: judge a loan on total cost and time, not the monthly payment; income-driven repayment is a safety net for unaffordable payments, not a default to reach for; forgiveness can be taxed; and refinancing a federal loan to a private one trades these protections away for good.