Calculate a loan's APR with fees by the Regulation Z actuarial method, the amount financed, the finance charge and the effective annual rate.
آخر تحديث أمثلة تم التحقق منها: 7
You receive $294,000.00 and repay 360 payments of $1,896.20, $682,633.47 in all. The rate that makes those payments worth exactly what you received is 0.5579% per period, an APR of 6.695%, against an interest rate of 6.5%. Compounded over a year, that is 6.905%.
| السنة | الفائدة | أصل القرض | الرصيد المتبقي |
|---|---|---|---|
| 1 | $19,401.27 | $3,353.18 | $296,646.82 |
| 2 | $19,176.70 | $3,577.74 | $293,069.08 |
| 3 | $18,937.10 | $3,817.35 | $289,251.73 |
| 4 | $18,681.44 | $4,073.01 | $285,178.72 |
| 5 | $18,408.66 | $4,345.79 | $280,832.93 |
| 6 | $18,117.62 | $4,636.83 | $276,196.10 |
| 7 | $17,807.08 | $4,947.37 | $271,248.73 |
| 8 | $17,475.75 | $5,278.70 | $265,970.03 |
| 9 | $17,122.22 | $5,632.23 | $260,337.81 |
| 10 | $16,745.02 | $6,009.43 | $254,328.38 |
Fees paid at closing or deducted from the proceeds are prepaid finance charges and come off the amount financed (12 CFR 1026.18(b)).
No closed form exists; the rate is bracketed by bisection and refined by Newton's method until the two sides agree to 28 decimal places.
12 CFR 1026 Appendix J (b)(1): the rate per unit-period times the unit-periods in a year.
Total of payments minus the amount financed: all interest plus the fees.
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.
مصدر التحقق: 12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %
مصدر التحقق: calculator.net APR calculator published result: real APR 6.563%, payment $1,110.21, total interest $33,224.60
مصدر التحقق: Python decimal (prec 60), bisection on the Appendix J equation to 400 halvings: APR 6.695317 %
مصدر التحقق: Definition: with no finance-charge fees the amount financed equals the loan; EAR 1.0058333^12 − 1 = 7.2290 %
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.
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.
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)).
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.
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.
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 %.
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.
للتخطيط فقط. يطبق المقرضون والسلطات الضريبية والأسواق قواعدهم الخاصة في التقريب والرسوم؛ تأكد من الأرقام لديهم قبل الالتزام.
تتضمن هذه الحاسبة أمثلة محلولة بإجابات من مصادر مستقلة، وعددها 7. تُشغّل ضمن مجموعة الاختبارات، ويمكنك تشغيلها هنا أيضًا.
احسب القسط الشهري لقرض سكني أو سيارة أو قرض شخصي، وإجمالي الفائدة، وجدول السداد الشهري مع الدفعات المبكرة.
قدّر الدفعة الشهرية مع ضريبة العقار والتأمين ورسوم جمعية الملاك (HOA) والتأمين العقاري الخاص (PMI)، وجدول السداد والتوفير من الدفعات الإضافية.
Compare refinancing at your planned sale or payoff month. See payments, closing costs, remaining balances and savings with cash or financed fees.
Calculate how long a credit card balance takes to pay off on minimum payments versus a fixed monthly payment, and the interest each costs.
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.
Compare the debt snowball (smallest balance first) and avalanche (highest rate first): months to debt-free, total interest and payoff order.