Lump Sum vs Annuity: Present-Value Crossover (2D)

Would you rather take a fixed sum today, or a stream of equal payments spread over the coming years? This simulator turns that classic finance question — the same one behind lottery payouts, structured settlements, and pension buyouts — into a 2D discounted cash-flow timeline and a live crossover chart. The timeline shows the lump sum sitting at time zero next to a bar for each future year's payment, its height shrinking the farther out it sits because it has been discounted back to today's dollars. The crossover chart plots the present value of both choices against every discount rate at once, so you can see directly where the two lines meet — the exact break-even rate — instead of hunting for it one slider tick at a time. Drag the discount rate and both views update live from the real present-value formulas, while a bisection solver reports the precise break-even rate.