# 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.

직접 계산할 수 있는 페이지: https://www.calcopenly.com/ko/finance/loan-affordability-calculator
분야: 금융 계산기

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.

## 입력

- **Monthly payment you can afford**
- **Interest rate (per year)**
- **Tenure**
- **Tenure in** (선택 항목: 년, 개월)
- **Down payment you have**

## 결과

- Loan you can afford — 주요 결과
- Price with your down payment
- Total of payments
- Total interest
- Number of payments

## 공식

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

## 계산 예제

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

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

## 자주 묻는 질문

### 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”의 정확도는 어느 정도인가요?

정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 4. 예를 들어 “500 a month for 20 years at 8%”은 Microsoft PV function documentation example: PV(0.08/12, 12*20, 500) = −59,777.15와 대조해 확인합니다.

### 이 계산 방법의 출처는 무엇인가요?

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

## 출처

- [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/)

_계획을 위한 참고용입니다. 대출기관, 세무당국과 시장은 자체 반올림 방식, 수수료와 규칙을 적용합니다. 계약 등의 결정을 내리기 전에 해당 기관에 수치를 확인하세요._