# APR calculator

> Calculate a loan's APR with fees by the Regulation Z actuarial method, the amount financed, the finance charge and the effective annual rate.

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

The APR is the yearly rate at which the loan payments are worth exactly the money you actually receive, the amount financed. Fees charged for the credit, such as origination fees and points, lower the amount financed when you pay them at closing, or raise the payments when they are added to the loan, so the APR comes out above the interest rate. The calculator solves for that rate numerically, as the actuarial method in Regulation Z, Appendix J, prescribes, and multiplies the rate per payment period by the periods in a year.

With the defaults, $300,000 at 6.5% for 30 years costs $1,896.20 a month. With $6,000 of fees paid upfront, the borrower receives $294,000, and the APR is 6.695%; the effective annual rate is 6.905%.

The APR assumes the loan runs to the end of its term with every payment on time. Paid off early, the fees are spread over fewer years and the true cost is higher.

## 输入

- **I know** (选项：The interest rate, The payment)
- **Loan amount**: Before any fees are added or deducted
- **Interest rate (per year)**
- **Payment each period**
- **Term**
- **Term in** (选项：年, 月)
- **Payments every** (选项：Week, Two weeks, Half-month, 月, Quarter, 年)
- **Fees in the finance charge**: Origination fees, points, broker fees and similar charges for the credit
- **Fees are** (选项：Paid at closing or deducted, Added to the loan)

## 结果

- 年百分率 — 主要结果
- Effective annual rate
- Interest rate implied by the payment
- Payment each period
- Amount financed
- Finance charge
- Total of payments
- Total interest

## 公式

$$
A_F = P\,\frac{1-(1+i)^{-n}}{i},\qquad \text{APR} = w\,i,\qquad \text{EAR} = (1+i)^{w}-1
$$

## 计算示例

### Regulation Z Appendix J (c)(1) example (i): $5,000, 24 monthly payments of $230

- I know: The payment
- Loan amount: 5000
- Payment each period: 230
- Term: 24
- Term in: 月
- Payments every: 月
- Fees in the finance charge: 0
- Fees are: Paid at closing or deducted
- **年百分率: 9.686%**
- 核验来源：12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %

### $100,000 at 6% for 10 years with $2,500 upfront fees

- I know: The interest rate
- Loan amount: 100,000
- Interest rate (per year): 6%
- Term: 10
- Term in: 年
- Payments every: 月
- Fees in the finance charge: 2500
- Fees are: Paid at closing or deducted
- **年百分率: 6.563%**
- **Payment each period: 1,110.21**
- **Amount financed: 97,500.00**
- **Total interest: 33,224.60**
- 核验来源：calculator.net APR calculator published result: real APR 6.563%, payment $1,110.21, total interest $33,224.60

### Defaults: $300,000 at 6.5% for 30 years, $6,000 upfront

- I know: The interest rate
- Loan amount: 300,000
- Interest rate (per year): 6.5%
- Term: 30
- Term in: 年
- Payments every: 月
- Fees in the finance charge: 6000
- Fees are: Paid at closing or deducted
- **年百分率: 6.695%**
- **Effective annual rate: 6.905%**
- **Payment each period: 1,896.20**
- **Finance charge: 388,633.47**
- 核验来源：Python decimal (prec 60), bisection on the Appendix J equation to 400 halvings: APR 6.695317 %

### No fees: APR equals the rate

- I know: The interest rate
- Loan amount: 20,000
- Interest rate (per year): 7%
- Term: 5
- Term in: 年
- Payments every: 月
- Fees in the finance charge: 0
- Fees are: Paid at closing or deducted
- **年百分率: 7.000%**
- **Effective annual rate: 7.229%**
- 核验来源：Definition: with no finance-charge fees the amount financed equals the loan; EAR 1.0058333^12 − 1 = 7.2290 %

### Fees added to the loan: $20,000 plus $800 at 9% for 3 years

- I know: The interest rate
- Loan amount: 20,000
- Interest rate (per year): 9%
- Term: 3
- Term in: 年
- Payments every: 月
- Fees in the finance charge: 800
- Fees are: Added to the loan
- **年百分率: 11.701%**
- **Payment each period: 661.43**
- **Total interest: 3,011.64**
- 核验来源：Python decimal: payment on 20,800, APR solved against the 20,000 received: 11.701083 %

### Zero-rate loan with a $300 fee

- I know: The interest rate
- Loan amount: 12,000
- Interest rate (per year): 0%
- Term: 12
- Term in: 月
- Payments every: 月
- Fees in the finance charge: 300
- Fees are: Paid at closing or deducted
- **年百分率: 4.700%**
- **Total interest: 0.00**
- **Finance charge: 300.00**
- 核验来源：Python decimal: 11,700 = 1,000 × a(12, i) gives i = 0.391671 %, APR 4.700046 %

## 常见问题

### What is the difference between APR and interest rate?

The interest rate sets the payment; the APR also counts fees charged for the credit and expresses the total cost as a yearly rate. A $100,000 loan at 6% for 10 years costs $1,110.21 a month; with $2,500 of upfront fees the borrower nets $97,500 and the APR is 6.563%. Without fees the APR equals the rate.

### How is APR calculated?

Find the rate per payment period at which the present value of all payments equals the amount financed, then multiply by the number of periods in a year. Regulation Z's Appendix J example: $5,000 repaid in 24 monthly payments of $230 gives a monthly rate of 0.80714%, so the APR is 9.69%. There is no closed formula, so the rate is found by iteration.

### Which fees are included in the APR?

Charges that are part of the finance charge under Regulation Z: points, loan and finder's fees, and premiums for insurance that protects the lender against default, such as mortgage insurance (12 CFR 1026.4(b)). Charges of a type you would pay in a cash deal are left out, and on real-estate loans so are bona fide title, appraisal, credit-report and document fees (1026.4(c)(7)).

### What is the difference between APR and effective annual rate?

The APR is the rate per period times the periods in a year, with no compounding; the effective annual rate compounds it: (1 + APR ÷ 12)^12 − 1 for monthly payments. A 6.695% APR on a monthly loan is an effective 6.905%. US disclosures use the APR; the effective rate is what the loan costs over a full year of compounding.

### How accurate does a lender's APR have to be?

Within 1/8 of a percentage point of the true APR for a regular loan, and within 1/4 point for irregular ones with multiple advances or uneven payments, under 12 CFR 1026.22(a). A disclosed APR of 6.75% on the default loan, whose true APR is 6.695%, is inside the tolerance; 6.85% is not.

### “APR 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：7。 例如，“Regulation Z Appendix J (c)(1) example (i): $5,000, 24 monthly payments of $230”根据12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %进行核验。

### 这种方法出自哪里？

12 CFR 1026, Appendix J (Regulation Z): annual percentage rate computations for closed-end credit; 12 CFR 1026.22: determination of the annual percentage rate and accuracy tolerances; 12 CFR 1026.18(b): amount financed; 12 CFR 1026.4: finance charge.

## 来源

- [12 CFR 1026, Appendix J (Regulation Z): annual percentage rate computations for closed-end credit](https://www.ecfr.gov/current/title-12/part-1026/appendix-Appendix%20J%20to%20Part%201026)
- [12 CFR 1026.22: determination of the annual percentage rate and accuracy tolerances](https://www.ecfr.gov/current/title-12/section-1026.22)
- [12 CFR 1026.18(b): amount financed](https://www.ecfr.gov/current/title-12/section-1026.18)
- [12 CFR 1026.4: finance charge](https://www.ecfr.gov/current/title-12/section-1026.4)

_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。_