# 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.

النسخة التفاعلية: https://www.calcopenly.com/ar/finance/apr-calculator
الموضوع: الحاسبات المالية

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.

## المدخلات

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

## النتائج

- معدل النسبة السنوية (⁨APR⁩) — النتيجة الرئيسية
- Effective annual rate
- Interest rate implied by the payment
- Payment each period
- Amount financed
- Finance charge
- Total of payments
- Total interest

## الصيغة

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

## أمثلة محلولة

### 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: أشهر
- Payments every: الشهر
- Fees in the finance charge: 0
- Fees are: Paid at closing or deducted
- **معدل النسبة السنوية (⁨APR⁩): 9.686%**
- مصدر التحقق: ⁨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: سنوات
- Payments every: الشهر
- Fees in the finance charge: 2500
- Fees are: Paid at closing or deducted
- **معدل النسبة السنوية (⁨APR⁩): 6.563%**
- **Payment each period: 1,110.21**
- **Amount financed: 97,500.00**
- **Total interest: 33,224.60**
- مصدر التحقق: ⁨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: سنوات
- Payments every: الشهر
- Fees in the finance charge: 6000
- Fees are: Paid at closing or deducted
- **معدل النسبة السنوية (⁨APR⁩): 6.695%**
- **Effective annual rate: 6.905%**
- **Payment each period: 1,896.20**
- **Finance charge: 388,633.47**
- مصدر التحقق: ⁨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: سنوات
- Payments every: الشهر
- Fees in the finance charge: 0
- Fees are: Paid at closing or deducted
- **معدل النسبة السنوية (⁨APR⁩): 7.000%**
- **Effective annual rate: 7.229%**
- مصدر التحقق: ⁨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: سنوات
- Payments every: الشهر
- Fees in the finance charge: 800
- Fees are: Added to the loan
- **معدل النسبة السنوية (⁨APR⁩): 11.701%**
- **Payment each period: 661.43**
- **Total interest: 3,011.64**
- مصدر التحقق: ⁨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: أشهر
- Payments every: الشهر
- Fees in the finance charge: 300
- Fees are: Paid at closing or deducted
- **معدل النسبة السنوية (⁨APR⁩): 4.700%**
- **Total interest: 0.00**
- **Finance charge: 300.00**
- مصدر التحقق: ⁨Python decimal: 11,700 = 1,000 × a(12, i) gives i = 0.391671 %, APR 4.700046 %⁩

## الأسئلة

### 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.

### ما مدى دقة «⁨APR calculator⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 7. مثلًا، يجري التحقق من «⁨Regulation Z Appendix J (c)(1) example (i): $5,000, 24 monthly payments of $230⁩» بالرجوع إلى ⁨12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %⁩.

### ما مصدر هذه الطريقة؟

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.

## المصادر

- [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)

_للتخطيط فقط. يطبق المقرضون والسلطات الضريبية والأسواق قواعدهم الخاصة في التقريب والرسوم؛ تأكد من الأرقام لديهم قبل الالتزام._