⏳ 货币时间价值计算器（TVM）Time Value of Money Calculator (TVM)
像金融计算器一样，在现值 PV、终值 FV、每期付款 PMT、期数 N 和年利率之间求解任意一项，支持期初/期末付款和每年复利次数，现金流符号遵循“流入为正、流出为负”。Solve for any one of present value, future value, payment, number of periods or annual rate — like a financial calculator — with payments at the beginning or end of each period and any compounding frequency. Cash outflows are negative, inflows positive.
使用说明与常见问题How-to & FAQ
「货币时间价值计算器（TVM）」是什么？What is the Time Value of Money Calculator (TVM) tool?
像金融计算器一样，在现值 PV、终值 FV、每期付款 PMT、期数 N 和年利率之间求解任意一项，支持期初/期末付款和每年复利次数，现金流符号遵循“流入为正、流出为负”。Solve for any one of present value, future value, payment, number of periods or annual rate — like a financial calculator — with payments at the beginning or end of each period and any compounding frequency. Cash outflows are negative, inflows positive.
如何使用「货币时间价值计算器（TVM）」？How do I use the Time Value of Money Calculator (TVM) tool?
在「货币时间价值计算器（TVM）」中，填写「求解」、「现值 PV」、「终值 FV」、「每期付款 PMT」、「期数 N」等参数，结果会随输入实时计算并显示在下方。In the Time Value of Money Calculator (TVM): Fill in "Solve for", "Present value PV", "Future value FV", "Payment PMT", "Number of periods N"; results are recalculated instantly as you type.
为什么有正负号？Why are some values negative?
与 BA II Plus、Excel FV/PV/PMT 函数相同：从你口袋里付出的钱为负，收到的钱为正，PV、PMT、FV 都可以填负数；年利率也可以为负（须大于 −100%）。例如存入 10,000 元（PV = −10,000）并每月再存 200（PMT = −200），到期取出的 FV 为正。Like a BA II Plus or Excel's FV/PV/PMT: money you pay out is negative and money you receive is positive, and PV, PMT and FV may all be negative; the annual rate may be negative too (above −100%). Depositing 10,000 (PV = −10,000) plus 200 a month (PMT = −200) gives a positive FV you withdraw.
公式是什么？What formula is used?
PV·(1+i)ⁿ + PMT·(1+i·d)·((1+i)ⁿ − 1)/i + FV = 0，其中 i = 年利率 ÷ 每年期数，d = 1 表示期初付款。求利率时用二分法数值求解。PV·(1+i)ⁿ + PMT·(1+i·d)·((1+i)ⁿ − 1)/i + FV = 0, where i = annual rate ÷ periods per year and d = 1 for payments at the beginning. The rate is solved numerically by bisection.
期初和期末有什么区别？Beginning vs end of period?
期末付款（普通年金）如房贷还款；期初付款（先付年金）如房租、保费。期初付款每笔多计一期利息，终值更大。End-of-period (ordinary annuity) suits loan payments; beginning-of-period (annuity due) suits rent or premiums. Paying at the beginning earns one extra period of interest on each payment.
计算结果可以作为最终依据吗？Can I rely on the result?
「货币时间价值计算器（TVM）」按标准公式计算，结果仅供参考；实际金额以银行、券商或税务机关的规则和四舍五入方式为准。The Time Value of Money Calculator (TVM) uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.
「货币时间价值计算器（TVM）」免费吗？需要注册吗？Is the Time Value of Money Calculator (TVM) free? Do I need an account?
「货币时间价值计算器（TVM）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Time Value of Money Calculator (TVM) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.