# Accurate APR Calculator

Calculates APR for Every Closed-End Example in Regulation Z, Appendix J

The annual percentage rate (APR) is a Very Important Number.

If you are a borrower, it is the one number you should use when comparing loan offers.

If you are a lender in the United States, you must disclose the APR by providing potential borrowers with a Regulation Z APR Disclosure Statement in order not to run afoul of the law. (See who must prepare a disclosure statement below.)

This calculator will calculate the APR for any closed-end loan as well as create a compliant Truth-in-Lending Act disclosure statement.

This post discusses what the APR is and why you should use it and not the interest rates to compare loans. I'll also instruct users on how to create a disclosure statement.

Let's get started. More below

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## What is Annual Percentage Rate or APR?

The Consumer Protection Financial Bureau paraphrases the Truth In Lending Act (TILA) of 1968, which says the "annual percentage rate is the cost of credit expressed as a yearly rate in a percentage."

### What is the difference between an interest rate and the annual percentage rate?

Again, I'll paraphrase from the CPFB:

A loan's interest rate is the cost you pay each year to borrow money expressed as a percentage. The interest rate does not include fees charged for the loan.

The annual percentage rate is the cost you pay each year to borrow money, including fees, expressed as a percentage. Therefore, the APR is (basically) the rate-of-return earned by the lender.

Rate-of-return?

Yes! From the lender's perspective. Remember, the loan is the lender's investment and all investor's hope to make a return.

What's important for the borrower to remember, is the lower the APR, the less the loan will cost, which makes sense. The lower the rate-of-return for the lender, the less profit they are earning on the loan they issue.

## Why should a borrower compare APRs and not interest rates?

The APR was created by the TILA to give borrowers a way to compare loans.

Why can't I just compare the interest rate of two loans and select the loan with the lowest rate?

Good question, and here's why.

If you wanted to compare two loans using their quoted interest rates, you would have to know and understand a lot of details about how the interest rate is used to calculate each loan's interest.

For example, you would have to know:

• each loan's compounding frequency;
• the days-per-year used for odd day interest calculations;
• the interest allocation method for short or long periods; and
• the impact of fees

Once you understand these details, then you would be able to calculate the interest due and compare the results.

Aside from fees, the APR isn't concerned with these details.

Why?

The APR calculation uses for input the anticipated total payment amounts. Periodic interest never is used in the equation.

Also, the TILA creates rules for how to calculate an APR. All disclosures have to use the same equations. This is not true for interest calculations.

This is why the APR is a Very Important Number.

But the APR is not the only thing that Regulation Z requires the lender to disclose.

## What disclosures does the TILA require?

The federal Truth-in-Lending Act requires that borrowers receive written disclosures about important terms of credit before they are legally bound to pay the loan.

In addition to the APR, the following must be prominently shown:

Finance Charge: cost of credit expressed as a dollar amount (this is the total amount of interest and certain fees you will pay over the life of the loan if you make every payment when due);

Amount Financed: the dollar amount of credit provided to you;

Total of Payments: the sum of all the payments that you will have made at the end of the loan (this includes repayment of the principal amount of the loan plus all of the finance charges)

The TILA disclosure will also include other important terms of the loan such as the number of payments, the monthly payment, late fees, whether you can prepay your loan without a penalty, and other important conditions. Exactly what must be included on the disclosure statement varies depending on the conditions of the loan itself.

The disclosure statement that this calculator creates is fully compliant with the TILA.

Alright, we've defined "APR," and we've covered at a high level what loan terms must be disclosed, but how do I use the calculator?

That question gets answered in the next section.

## Using the APR calculator

The annual percentage rate calculation, as Regulation Z documents it in Appendix J, does not care about pesky details.

The calculation does not need to know what the loan's compounding frequency is. It does not care if the loan uses 360 or 365 day years. It does not care if the interest is calculated using the same day months or calculated using the exact number of days in a month.

What the calculation requires is the following:

• The loan amount or amounts
• The payment schedule, meaning the loan's principal and interest payment amounts and when they are due. (These loan payments do NOT include any charges or fees.)
• The fees or charges the lender requires the borrower to pay.

Using these details, the calculator will calculate the four values lenders must reveal.

• Amount Financed
• Finance Charge
• Annual Percentage Rate
• Total of Payments

The amount financed is calculated by determining the principal loan amount and adding any other amounts that are financed by the creditor and are not part of the finance charge, and subtracting any prepaid finance charges such as prepaid interest and loan application fees.

The finance charge is the cost of consumer credit as a dollar amount. It includes any charge payable directly or indirectly by the consumer and imposed directly or indirectly by the creditor as an incident to or a condition of the extension of credit. Note, however, finance charges do not include any charge of a type payable in a comparable cash transaction.

Finance charges include but are not limited to the following (as quoted from 226.4 of Reg. Z):

• (1) Interest, time price differential, and any amount payable under an add-on or discount system of additional charges.
• (2) Service, transaction, activity, and carrying charges, including any charge imposed on a checking or other transaction account to the extent that the charge exceeds the charge for a similar account without a credit feature.
• (3) Points, loan fees, assumption fees, finder’s fees, and similar charges.
• (4) Appraisal, investigation, and credit report fees.
• (5) Premiums or other charges for any guarantee or insurance protecting the creditor against the consumer’s default or other credit loss.
• (6) Charges imposed on a creditor by another person for purchasing or accepting a consumer’s obligation, if the consumer is required to pay the charges in cash, as an addition to the obligation, or as a deduction from the proceeds of the obligation.
• (7) Premiums or other charges for credit life, accident, health, or loss-of-income insurance, written in connection with a credit transaction.
• (8) Premiums or other charges for insurance against loss of or damage to property, or against liability arising out of the ownership or use of property, written in connection with a credit transaction.
• (9) Discounts for the purpose of inducing payment by a means other than the use of credit.
• (10) Charges or premiums paid for debt cancellation or debt suspension coverage written in connection with a credit transaction, whether or not the coverage is insurance under applicable law.

### Prepaid Interest

A special note about prepaid interest. Loans can and will close on any day of the month, not just on a payment due date. If payments are due on the first and a loan closes (loan amount is made available) on the twenty-sixth, the first payment frequently will not be due until the first of the 2nd month following the closing. That is, if the loan closes on July 26 the first payment will be due on September 1. The time between the loan closing and the first payment is longer than a month. This is called a long initial period. The lender is going to want the interest they are entitled to for these 6 days (July 26 - August 1). They can collect the interest for the 6 days by adding it to the September 1 payment. Or, they can ask for the interest on the day the loan closes. If they collect it on the day the loan closes, this is prepaid interest.

You can use this interest calculator to calculate exact day prepaid interest.

But here's a tip. When it's all said and done, an APR disclosure statement is almost always just an estimate since it has to be given to the borrower even prior to the loan closing. Frequently the closing date isn't even known when the disclosure is provided. Therefore, keep it simple, and just assume regular length periods!

But with that said...

If the software used to calculate the APR is not accurate, the lender may be subject to fines and adverse publicity leading to reputational damage.

The next section will prove to you the accuracy of this calculator.

## All the example from Regulation Z, Appendix J

Lenders and borrowers need to have confidence in the tools they use.

Is there any better way to prove the accuracy and flexibility of this calculator than to give the user the ability to quickly load each of the 20 calculations from Regulation Z, Appendix J, and allow them to calculate the results?

Of course not.

Click on the links below to preload the calculator with the inputs specified by the particular example. You can then click on "Calc" and compare the result with the result defined in the regulation.

Skeptical? Change one of the inputs and recalculate. You'll see the APR result change.

Not only does this confirm the accuracy of this calculator, but it also shows its flexibility. It handles every closed-end loan examples with multiple loan advances such as construction loans and student loans. (I have not found another calculator on the web that can do these calculations.)

Go ahead, try a few examples. Remember, just click on a link and the details will be preloaded for you in the calculator. No need for manual entry!

### The Examples

Regulation Z classifies the following five examples as "(1) Single advance transaction, with or without an odd first period, and otherwise regular."

1. Example (i): Monthly payment (regular first period)
• Amount advanced = \$5,000. Payment = \$230.
• Number of payment = 24.
• Loan advance 01/10/1978 First payment 02/10/1978.
• APR = 9.69%
2. Example (ii): Monthly payments (long first period)
• Amount advanced = \$6,000. Payment = \$200.
• Number of payments = 36.
• Loan advance 02/10/1978 First payment 04/01/1978
• APR = 11.82%
3. Example (iii): Semimonthly payments (short first period)
• Amount advanced = \$5,000. Payment = \$219.17.
• Number of payments = 24.
• Loan advance 02/23/1978. First payment 03/01/1978
• Payments made on 1st and 16th of each month.
• APR = 10.34%
4. Example (iv): Quarterly payments (long first period)
• Amount advanced = \$10,000. Payment = 385.
• Number of payments = 40
• Loan advance = 05/23/1978. First payment = 10/01/1978
• APR = 8.97%
5. Example (v): Weekly payments (long first period)
• Amount advanced = \$500. Payment = 17.60
• Number of payments = 30.
• Loan advance on 03/20/1978. First payment on 04/21/1978
• APR = 14.96%.

Regulation Z classifies the following two examples as "(2) Single advance transaction, with an odd first payment, with or without and odd first period, and otherwise regular."

1. Example (i): Monthly payments (regular first period and irregular first payment)
• Amount advanced = \$5,000. First payment = \$250. Regular payment = \$230.
• Number of payments = 24.
• Loan advance on 01/10/1978. First payment on 02/10/1978
• APR = 10.08
2. Example (ii): Payments every 4 weeks (long first period and irregular first payment)
• Amount advanced = \$400. First payment = \$39.50
• Regular payment = \$38.31. Number of payments = 12.
• Loan advance on 03/18/1978. First payment on 04/20/1978.
• APR = 28.50%

Regulation Z classifies the following two examples as "(3) Single advance transaction, with an odd final payment, with or without an odd first period, and otherwise regular."

1. Example (i): Monthly payments (regular first period and irregular final payment)
• Amount advanced = \$5,000. Regular payment = \$230.
• Final payment = \$280. Number of payments = 24.
• Loan advance on 01/10/1978. First payment on 02/10/1978
• APR = 10.50%
2. Example (ii): Payments every 2 weeks (short first period and irregular final payment)
• Amount advanced = \$200. Regular payment = \$9.50.
• Final payment = \$30. Number of payments = 20.
• Loan advance on 04/03/1978. First payment on 04/11/1978
• APR = 12.22%

Regulation Z classifies the following two examples as "(4) Single advance transaction, with an odd first payment, odd final payment, with or without an odd first period, and otherwise regular."

1. Example (i): Monthly payments (regular first period, irregular first payment, and irregular final payment)
• Amount advanced = \$5,000. First payment = \$250. Regular payment = \$230.
• Final payment = \$280. Number of payments = 24.
• Loan advance on 01/10/1978. First payment on 02/10/1978.
• APR = 10.90%
2. Example (ii): Payments every two months (short first period, irregular first payment, and irregular final payment)
• Amount advanced = \$8,000. First payment = \$449.36.
• Regular payment = \$465. Final payment = \$200. Number of payments = 20.
• Loan advance on 01/10/1978. First payment on 03/01/1978.
• APR = 7.30%

Regulation Z classifies the following four examples as "(5) Single advance, single payment transaction."

1. Example (i): Single advance, single payment (term of less than 1 year, measured in days)
• Amount advanced = \$1,000. Payment = 1080.
• Loan advance on 01/03/1978. Payment on 09/15/1978.
• APR = 11.45%
2. Example (ii): Single advance, single payment (term of less than 1 year, measured in exact calendar months)
• Amount advanced = \$1,000. Payment = \$1044.
• Loan advance on 07/15/1978. Payment on 1/15/1979
• APR = 8.80%
3. Example (iii): Single advance, single payment (term of more than 1 year but less than 2 years, fraction measured in exact months)
• Amount advanced = \$1,000. Payment = \$1,135.19.
• Loan advance on 01/17/1978. Payment on 01/17/1980.
• APR = 8.76%
4. Example (iv): Single advance, single payment (term of exactly 2 years)
• Amount advanced = \$1,000. Payment = \$1,240.
• Loan advance on 01/03/1978. Payment on 01/03/1980.
• APR = 11.36%

Regulation Z classifies the following three examples as "(6) Complex single advance transaction."

1. Example (i): Skipped payment loan (payments every 4 weeks)
• Amount advanced = \$2135. Payment = \$100.
• Number of payments = 24. Payments are due every 4 weeks. However, in those months in which 2 payments would be due, only the first of the 2 payments is made and the following payment is delayed by 2 weeks to place it in the next month.
• Loan advance on 01/25/1978. First payment on 02/20/1978.
• APR = 12.00%
2. Example (ii): Skipped payment loan plus single payments
• Payment = \$1,000. Number of payments = 3. Payment on 09/15/1978.
• Payment = \$2,000. Number of payments = 1. Payment on 03/15/1979.
• Payment = \$750. Number of payments = 3. Payment on 09/15/1979.
• Payment = \$1,000. Number of payments = 1. Payment on 02/01/1980.
• APR = 10.22%
3. Example (iii): Mortgage with varying monthly payments
• Amount advanced (net) = \$39.688.56.
• Number of payments = 360.
• Loan advance on 04/10/1978. Payment on 06/01/1978.
• Payments are the same for 12 months at a time.
•  Year MonthlyPayment Year MonthlyPayment Year MonthlyPayment 1 \$291.81 11 \$385.76 21 \$380.43 2 300.18 12 385.42 22 379.60 3 308.78 13 385.03 23 378.68 4 317.61 14 384.62 24 377.69 5 326.65 15 384.17 25 376.60 6 335.92 16 383.67 26 375.42 7 345.42 17 383.13 27 374.13 8 355.15 18 382.54 28 372.72 9 365.12 19 381.90 29 371.18 10 375.33 20 381.20 30 369.50
• APR = 9.80%

Regulation Z classifies the following two examples as "(7) Multiple advance transactions."

1. Example (i): Construction loan (3 loan advances followed by monthly payments)
• Amount advanced = \$20,000 each.
• Loan advances on 04/10/1979, 06/12/1979, and 09/18/1979.
• Payment = \$612.36. Number of payments = 240.
• Payment on 12/10/1979.
• APR = 10.25%
2. Example (ii): Student loan (8 loan advances, monthly payment, and the first payment before first advance)
• Payment = \$240. Number of payments = 50. Payment on 07/01/1978.
• Amount advance = \$1,800 on 09/05/78.
• Amount advance = \$1,000 on 01/05/79.
• Amount advance = \$1,800 on 09/05/79.
• Amount advance = \$1,000 on 01/05/80.
• Amount advance = \$1,800 on 09/05/80.
• Amount advance = \$1,000 on 01/05/81.
• Amount advance = \$1,800 on 09/05/81.
• Amount advance = \$1,000 on 01/05/82.
• APR = 32.04%

## Who must prepare a disclosure statement?

A lender, whether that lender is a business or an individual must comply with the Truth-in-Lending-Act and provide the borrower with a disclosure statement prior to offering or extending credit when four conditions are met:

1. The credit is offered or extended to consumers;
2. The lender offers or extends credit regularly;
3. The credit is subject to a finance charge or is payable by a written agreement in more than four installments; and
4. The credit is primarily for personal, family, or household purposes.

## Wrapping Up

As you can see, there is a lot to understanding the Truth-In-Lending Act and an APR Disclosure Statement.

However, if you are a borrower, and you are comparing loan options, just compare the APRs. And assuming the lenders are of similar quality and offer the same or similar services, go with the loan that has the lower APR.

## 28 Comments on “APR Calculator”

Join the conversation. Tell me what you think.
• ##### Lisl Unterholznersays:

Your excellent article states: The Consumer Protection Financial Bureau paraphrases the Truth In Lending Act (TILA) of 1968, which says the “annual percentage rate is the cost of credit expressed as a yearly rate in a percentage.”

And the disclosures require the total amount of payments, the total finance charges and the amount financed. There doesn’t seem to be a clear relationship between those three numbers and the APR.
The math in Appendix J looks fairly complicated.
It seems like you should be able to look at the amount of interest you are going to pay and the number of years in relation to the amount financed and get a more straightforward relationship/percentage. Is there something I’m missing about how to interpret APR?

• ##### Karlsays:

I think that you have the idea, except the unit period is not always the year as you are suggesting. A lot of the complexity comes in when the cash flow is irregular or the amounts change. If you want more details, read about the "Unit Period" in Appendix J.