RETIREMENT LABCONSUMER MATH · 3.9
TIME. CONTRIBUTIONS. COMPOUND GROWTH.

给未来的自己,一份计划。A plan for your future self.

从每月的一笔投入开始,看看时间、通胀与养老金如何改变退休目标。Explore how time, inflation and pension income change the amount you need to save.

选择一个起点Choose a starting point

从积累,到支取From saving to spending

如果只改变一件事?Change one assumption.

以下是独立实验,每次只调整标注的变量。Each experiment changes only the stated assumption.

并排比较两个方案Compare two plans

逐年明细Year-by-year projection

课堂探索:从原活动继续往前走Classroom challenges
投入更多,还是工作更久?Save more or work longer?

载入 Lucía。记录每月投入 500 的方案,再试 750、1,000;恢复 500,将退休年龄改为 70。哪种改变更可行?说明代价。Load Lucía. Save the $500/month baseline, then try $750 and $1,000. Restore $500 and retire at 70. Compare the trade-offs.

开始得早,究竟赢在哪里?What does starting early change?

载入 Daniel。先预测推迟 5 年投入会损失多少,再查看实验结果。缺失的不只是本金,还有哪些收益?Load Daniel. Predict the cost of delaying contributions for five years. What is lost besides the deposits themselves?

有养老金,还需要自己投资吗?How does a pension change the goal?

切到中国场景,先记录养老金为 0 的结果;再填入一个课堂假设金额。将领取年龄延后,或取消随通胀增长,观察资金缺口。Switch to China and save a zero-pension baseline. Add an assumed pension, then delay its start or turn off inflation indexation.

理解公式、假设与中美场景Understand the model and country scenarios

01 · 与原活动一致的年度模型Annual model aligned with the activity

每月投入是第一年的月均金额;全年投入汇总到年末。工资和投入按设置的增长率逐年增长。现有余额先获得当年回报,再加当年投入。The monthly contribution is the first-year monthly amount. Annual deposits occur at year-end and grow with salary each year. The opening balance earns a return before deposits are added.

下一年余额 = 本年余额 × (1 + 年回报率) + 个人年投入 + 雇主年投入Next balance = opening balance × (1 + annual return) + employee + employer deposits

这不是按月复利模型。美国原活动案例默认:退休前 6%、退休后 5%、通胀 3%、工资与投入增长 2%;养老金和雇主配比均为 0。This is not monthly compounding. US activity profiles use 6% before retirement, 5% after, 3% inflation and 2% salary/deposit growth; pension and employer match start at zero.

02 · 退休目标怎样算?How is the required fund calculated?

月预算和养老金均以今天的购买力输入。预算随通胀上涨;退休目标是每年“支出 − 养老金”的正缺口折现值之和。养老金超过支出的部分不再投资。Budget and pension inputs are in today's money. Spending rises with inflation. The target is the present value of each positive spending-minus-pension gap; pension surpluses are not reinvested.

退休目标 = Σ 每年资金缺口 ÷ (1 + 退休后回报率)付款序号Required fund = Σ annual shortfall ÷ (1 + post-retirement return)payment number

退休后也是先计算回报,再于年末支取。覆盖至 95 岁包含 95 岁这一整年;67 岁退休对应 29 次年度支取,最后的年末余额标在 96 岁。Retirement withdrawals occur at year-end after growth. Funding through age 95 includes that entire year: retirement at 67 means 29 withdrawals, with the last ending balance shown at age 96.

03 · 名义金额与购买力Nominal money vs. purchasing power

今天购买力 = 未来金额 ÷ (1 + 通胀率)距离现在的年数Today's money = future money ÷ (1 + inflation)years from now

切换显示口径会同时调整目标、预计余额和曲线。所需“初始每月投入”仍是第一年实际要投入的金额。逐年 CSV 始终保留名义金额。The display switch adjusts both the target and projected balances. Required initial monthly contributions remain first-year amounts. CSV exports always retain nominal money.

04 · 养老金与雇主投入Pensions and employer contributions

养老金在设定的领取年龄才开始抵扣退休支出。首次领取金额由今天购买力换算;此后可选择随通胀调整,或保持名义金额不变。这里只计退休后的领取。Pensions offset spending only during retirement and from the selected claim age. The first payment is inflated from today's money; later payments can track inflation or remain nominally fixed.

雇主配比 = 配比比例 × min(个人年投入,年工资 × 配比上限)。中国企业年金选项使用相同的课堂模拟规则,不代表任何单位的实际制度。Employer match = match rate × min(employee annual deposits, salary × match cap). The China annuity option uses this classroom rule, not a statutory or employer-specific formula.

这些是可修改的教学假设,不是收益预测或养老金待遇核定。模型未计税费、市场波动、账户缴费限额与突发支出;充足率表示预计资金相对于目标的比例,不是成功概率。当前方案只保留在本页,刷新即重置。This educational model uses editable assumptions, not return forecasts or pension eligibility calculations. It excludes taxes, fees, market volatility, account limits and unexpected expenses. Funding coverage is a ratio, not a probability of success. Plans reset when the page is refreshed.