# 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.

Phiên bản tương tác: https://www.calcopenly.com/vi/finance/loan-affordability-calculator
Chủ đề: Máy tính tài chính

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.

## Dữ liệu đầu vào

- **Monthly payment you can afford**
- **Interest rate (per year)**
- **Tenure**
- **Tenure in** (lựa chọn: Năm, Tháng)
- **Down payment you have**

## Kết quả

- Loan you can afford — kết quả chính
- Price with your down payment
- Total of payments
- Total interest
- Number of payments

## Công thức

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

## Ví dụ có lời giải

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

- Monthly payment you can afford: 500
- Interest rate (per year): 8%
- Tenure: 20
- Tenure in: Năm
- Down payment you have: 0
- **Loan you can afford: 59,777.15**
- **Total interest: 60,222.85**
- Nguồn đối chiếu: 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: Năm
- Down payment you have: 50,000
- **Loan you can afford: 186,198.20**
- **Price with your down payment: 236,198.20**
- Nguồn đối chiếu: 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: Tháng
- Down payment you have: 0
- **Loan you can afford: 12,000.00**
- **Total interest: 0.00**
- Nguồn đối chiếu: 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: Tháng
- Down payment you have: 0
- **Loan you can afford: 1,000.00**
- **Total interest: 10.00**
- Nguồn đối chiếu: 1010 / 1.01 by hand

## Câu hỏi

### 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” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 4. Ví dụ, “500 a month for 20 years at 8%” được kiểm tra bằng Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15.

### Phương pháp này lấy từ đâu?

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

## Nguồn

- [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/)

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