Calculate a loan's APR with fees by the Regulation Z actuarial method, the amount financed, the finance charge and the effective annual rate.
更新日 検証済みの例：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%.
| 年 | 利息 | 元金 | 残高 |
|---|---|---|---|
| 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.
照合元：12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %
照合元：calculator.net APR calculator published result: real APR 6.563%, payment $1,110.21, total interest $33,224.60
照合元：Python decimal (prec 60), bisection on the Appendix J equation to 400 halvings: APR 6.695317 %
照合元：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.
精度は入力値と計算方法の前提に依存します。十進演算には有効数字50桁を使いますが、推定、数値計算手法、元データの精度はそれより低い場合があります。表示の丸め処理でこれらの制約がなくなるわけではありません。 独立した出典の解答と照合した計算例：7。 例えば、「Regulation Z Appendix J (c)(1) example (i): $5,000, 24 monthly payments of $230」は12 CFR 1026 Appendix J, (c)(1) Example (i): annual percentage rate 9.69%; Python decimal gives 9.685708 %と照合しています。
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.
計画の参考用です。金融機関、税務当局、市場は独自の丸め方、手数料、規則を適用します。契約などの前に該当機関へ金額を確認してください。
この計算機には、独立した出典の解答を使った計算例が 7 件あります。テストに組み込まれており、ここでも実行できます。
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