What this calculator does
This is a car affordability calculator that works backwards. Instead of starting with a car price and telling you the monthly payment, you start with the monthly payment you are comfortable with and it tells you the maximum car price you can afford. It also shows the loan amount you would need to borrow and a clear breakdown of how the price, sales tax, down payment and trade-in fit together. The sales-tax rules used here follow the US model.
How to use it
Enter the monthly payment you want to make, your sales-tax rate, any down payment and trade-in value, the loan term (in months or years), and the annual interest rate (APR). The tool returns the affordable car price and the car loan you would need. Adjust the payment up or down to instantly see how much more or less car you can afford.
The formula explained
First we convert your target monthly payment into a loan principal using the present value of an ordinary annuity:
Next we turn that loan into a car price. The loan must cover the car price plus sales tax, minus your down payment and trade-in: Loan = Price×(1+t)-Down-Trade. Rearranging gives
Assumption: this tool applies sales tax to the full car price. Some US states tax only the price minus the trade-in; if that applies to you, your actual tax will be a little lower.
Worked example
Suppose you want a 425 monthly payment, a 48-month term, 2.5% APR, 6% sales tax,2,000 down and a 1,500 trade-in. The monthly rate is 0.025 / 12 = 0.0020833. The loan principal is
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。