# Loan affordability calculator

> Find how much you can borrow from the monthly payment you can afford at your rate and term, and the price your down payment then buys.

交互版本：https://www.calcopenly.com/zh/finance/loan-affordability-calculator
主题：财务计算器

This works the EMI formula backwards. Given the monthly payment you can afford, the largest loan it repays is P = M × (1 − (1 + r)^−n) ÷ r, where r is the monthly rate and n the number of payments; this is what Excel's PV function returns. Adding your down payment gives the highest price you can pay.

With the defaults, 1,500 a month for 20 years at 7.5% supports a loan of 186,198.20, and 50,000 down lifts the price you can afford to 236,198.20. The 240 payments total 360,000.00, of which 173,801.80 is interest.

The result is the ceiling your budget sets. Lenders also limit the payment by your income through the debt-to-income ratio, and property tax, insurance and fees come out of the same monthly budget.

## 输入

- **Monthly payment you can afford**
- **Interest rate (per year)**
- **Tenure**
- **Tenure in** (选项：年, 月)
- **Down payment you have**

## 结果

- Loan you can afford — 主要结果
- Price with your down payment
- Total of payments
- Total interest
- Number of payments

## 公式

$$
P = M \cdot \frac{1 - (1+r)^{-n}}{r},\qquad r = \frac{\text{annual rate}}{1200}
$$

## 计算示例

### 500 a month for 20 years at 8%

- Monthly payment you can afford: 500
- Interest rate (per year): 8%
- Tenure: 20
- Tenure in: 年
- Down payment you have: 0
- **Loan you can afford: 59,777.15**
- **Total interest: 60,222.85**
- 核验来源：Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15

### 1,500 a month for 20 years at 7.5% with 50k down

- Monthly payment you can afford: 1500
- Interest rate (per year): 7.5%
- Tenure: 20
- Tenure in: 年
- Down payment you have: 50,000
- **Loan you can afford: 186,198.20**
- **Price with your down payment: 236,198.20**
- 核验来源：Python decimal (prec 50) present value of an ordinary annuity

### Zero rate

- Monthly payment you can afford: 1000
- Interest rate (per year): 0%
- Tenure: 12
- Tenure in: 月
- Down payment you have: 0
- **Loan you can afford: 12,000.00**
- **Total interest: 0.00**
- 核验来源：M × n when there is no interest

### One month at 12%

- Monthly payment you can afford: 1010
- Interest rate (per year): 12%
- Tenure: 1
- Tenure in: 月
- Down payment you have: 0
- **Loan you can afford: 1,000.00**
- **Total interest: 10.00**
- 核验来源：1010 / 1.01 by hand

## 常见问题

### How much can I borrow with a given monthly payment?

Multiply the payment by the annuity factor (1 − (1 + r)^−n) ÷ r. At 8% over 20 years, r = 0.08 ÷ 12 and n = 240, so the factor is 119.55 and a payment of 500 a month supports a loan of 59,777.15. Microsoft's documentation for Excel's PV function gives the same figure for PV(0.08/12, 240, 500).

### What debt-to-income ratio do lenders accept?

In the US, the CFPB suggests keeping total debt payments at 36% of gross monthly income or less and housing costs at 28% to 35%, though some lenders go to 43% or higher. Fannie Mae's standard maximum is 36%, rising to 45% with credit-score and reserve requirements and to 50% for loans underwritten through Desktop Underwriter. On a gross income of 5,000 a month, 36% is 1,800.

### How does the interest rate change how much I can borrow?

A higher rate means more of each payment goes to interest, so the same payment supports a smaller loan. Over 20 years, 1,500 a month supports 201,187.51 at 6.5%, 186,198.20 at 7.5% and 172,846.26 at 8.5%: each percentage point costs about 7% of the loan. The chart shows the full curve for your payment and term.

### Does a longer loan term let me borrow more?

Yes, but with diminishing returns and much more interest. At 7.5%, 1,500 a month supports 161,810.14 over 15 years, 186,198.20 over 20 years and 214,526.44 over 30 years. Going from 20 to 30 years adds 28,328.24 of borrowing but raises total interest from 173,801.80 to 325,473.56.

### “Loan affordability calculator”有多准确？

准确性取决于输入值和方法的假设。十进制运算使用50位有效数字，但估算、数值方法和源数据的精度可能较低；显示时的舍入并不能消除这些限制。 已按独立来源核验的计算示例：4。 例如，“500 a month for 20 years at 8%”根据Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15进行核验。

### 这种方法出自哪里？

Microsoft Excel PV function; Consumer Financial Protection Bureau — Debt-to-income ratio.

## 来源

- [Microsoft Excel PV function](https://support.microsoft.com/office/pv-function-23879d31-0e02-4321-be01-da16e8168cbd)
- [Consumer Financial Protection Bureau — Debt-to-income ratio](https://www.consumerfinance.gov/ask-cfpb/what-is-a-debt-to-income-ratio-en-1791/)

_仅用于规划。贷款机构、税务机关和市场采用各自的舍入方式、费用和规则；作出承诺前，请向相关机构确认数值。_