在線即時計算器 · 純前端本地秒算 · 零數據上傳

🪙 即期年金計算機

專業免費的 即期年金計算機。純前端本機毫秒級計算、零資料上傳、極致隱私保護。提供詳細公式推導、實例示範與常見問答。

即時推算結果 (Computed Output)
$659.96 per payment
專業公認計算模型,即時運算完畢
📜 計算歷史記錄 (試算軌跡)
尚無歷史記錄,每次點擊「計算」將在此留下試算軌跡...

What Is an Immediate Annuity Calculator?

An immediate annuity (also called a single-premium immediate annuity, or SPIA) converts a lump sum of money into a stream of guaranteed periodic income payments that begin right away. This calculator estimates how much income you would receive each period based on your premium, an assumed interest rate, the length of the payout, and how often payments are made.

How to Use It

Enter the principal (the lump sum or premium you pay), the assumed annual interest rate the insurer credits, the payout period in years, and the payment frequency (monthly, quarterly, semi-annual, or annual). The calculator returns the income per payment, the number of payments, the total payout, and the total interest earned over the contract.

The Formula Explained

The payment is the standard annuity (amortization) formula:

PMT = ((PV · r) ÷ (1 - (1 + r)^{-n}))
Here PV is the present value (your premium), r is the periodic interest rate (annual rate ÷ payments per year), and n is the total number of payments (years × payments per year). When the rate is zero, the payment simply equals PV ÷ n.

Worked Example

Suppose you pay a 100,000 premium for an annuity earning 5% annually, paid monthly over 20 years. The periodic rate is 0.05 ÷ 12 = 0.0041667 and there are 240 payments.

PMT = ((100,000 × 0.0041667) ÷ (1 - 1.0041667^{-240})) ≈659.96 per month
for a total payout of about 158,389 — roughly58,389 in interest.

使用注意事項與精準校對原則(6 大核心守則)

📐 1. 嚴格對齊輸入量綱與單位

輸入各項數值時請務必確認量綱(例如小時、天數、金額、百分比),避免單位不匹配引發推算偏差。

🔒 2. 純前端本機毫秒級隱私保障

所有計算邏輯 100% 在您的終端瀏覽器內完成,資料絕不上傳伺服器,嚴格守護商業與個人隱私。

📊 3. 符合公認學術與產業計算模型

演算法嚴格遵循國際通用數學公式與標準計算模型,經多重情境交叉核對,數值嚴密精確。

📋 4. 一鍵複製與免登入 PDF 匯出

支援一鍵複製推算結果字串至剪貼簿,亦可直接點擊列印按鈕輸出純淨 PDF 工作報表。

🔄 5. 多情景敏感度動態對比

建議針對極端值與多組預期情景分別試算,觀察輸出數據的波動區間,輔助做出更穩健的決策。

🛡️ 6. 專業諮詢與日常參考免責聲明

本工具運算結果供日常排程、學業研習與事前參考之用,如涉及重大法規或投資決策請諮詢持證專家。

常見問題 (FAQ)

Is this guaranteed income?
The calculator shows a math estimate. Actual insurer quotes depend on age, gender, mortality assumptions, fees, and current rates.
Does it account for inflation?
No — it models a fixed (non-indexed) annuity. Inflation-adjusted annuities pay less initially.
What rate should I use?
Use a rate near what insurers are currently crediting (often 3%–6%) for a realistic estimate.