Covers the purpose of the APR, how it is calculated, who can rely on it safely, who should not use it, and the various biases in the measure and how they could be removed.

Tutorial on Annual Percentage Rate (APR)

Last Revised August 8, 2010 

What Is the APR?


APR is a measure of the cost of credit that includes loan fees paid to the lender upfront, as well as the interest rate. The higher are the loan fees, the larger will be the APR relative to the rate. If there are no loan fees and the rate is fixed through the life of the loan, the APR will equal the rate.

What Is the Purpose of the APR?


To provide a single comprehensive measure of the cost of credit to the borrower, which they can use to compare loans of different types and features, and loans offered by different loan providers.

The APR is a mandated disclosure under Truth in Lending. Mortgage shoppers confront it as soon as they search for interest rate quotes, because the law requires that any rate quote must also show the APR.

Can All Borrowers Rely Safely on the APR?


No, some should ignore the APR, including:

* Borrowers who expect that they will sell their house or refinance the mortgage within 7 years.
* Borrowers looking to raise cash, who are comparing the cost of a cash-out refinancing with the cost of a second mortgage.
* Borrowers with little cash who need a high-rate loan with negative points (rebates) to cover their costs.
* Borrowers shopping for a home equity line of credit (HELOC).

The APR is most useful for borrowers shopping for an adjustable rate mortgage (ARM), who expect to hold the mortgage a long time, and who are not doing a cash-out refinance, a low or no-cost mortgage, or a HELOC.

Why Should Borrowers Who Expect To Have Their Mortgage Less Than 7 Years Ignore The APR?


Because over short periods, the APR is biased in favor of loans with low interest rates and high fees.

The APR combines fees paid upfront with interest paid every month. It does this by dividing the fees over the future life of the mortgage. In any month, the interest payment, plus the upfront fees allocated to that month, divided by the loan balance at the end of the preceding month, equals the APR. See Annual Percentage Rate Simplified.

In allocating the fees, it is assumed that the loan runs to term. A 30-year loan runs for 30 years, for example, and a 15-year loan runs for 15 years. This is contrary to fact, most loans are paid off well before term. While data on mortgage life are sketchy, the average life of 30-year loans today is certainly below 7 years.

The assumption that loans run to term reduces the fees allocated to each month, reducing the APR relative to what it would be if the loan was paid off before term. This imparts a bias in favor of loans with low interest rates and high fees.

For example, in shopping for a $200,000 30-year fixed-rate loan, Jones is offered 7% with $5500 in fees and APR of 7.28%, versus 6.5% with $11,500 in fees and APR of 7.08%. A comparison of APRs suggests that the 6.5% loan will cost less.

However, if Jones sells the house or refinances after 7 years, the APRs calculated over 7 years would be 7.53% for the 7% loan and 7.61% for the 6.5 % loan. The conclusion regarding the least costly loan is reversed.

If fees are about the same, this bias in the APR disappears. On fixed-rate mortgages (FRMs), however, the borrower can compare rates and doesn’t need the APR. On ARMs, in contrast, the APR can be useful, as noted below.

 Could This Bias in the APR Be Eliminated?


Yes, the bias could be eliminated by making the time period used in the calculation "borrower specific" -- calculated for each borrower over the period specified by the borrower. It takes only a minor tweak in the computer programs used to calculate APR to make the time period borrower specific. Where the borrower has not yet been identified, as in newspaper ads, several APRs could be shown, e.g., 3 years, 7 years and term.

Why Should the APR on a Cash-Out Refinancing Be Ignored?


Because it fails to take account of the rate on the old mortgage that is refinanced.

If the rate on the old mortgage is below the rate on the new larger mortgage, failure to account for the loss of the lower rate can falsely suggest that the cash-out refinance will cost less than a second mortgage that raises the same amount of cash.

For example, a borrower has a 7.5% mortgage with balance of $160,000 and needs to raise $20,000. The rate on a cash-out refinance for $180,000 is 8%, and if there are no fees, the APR is 8%. The rate on a second mortgage of $20,000 is 9% and if there are no fees, the APR is 9%. A comparison of APRs suggests that the cash-out refinance is cheaper, but it isn’t. The APR of 8% does not account for the 1/2% increase on $160,000 which would be avoided by selecting the second mortgage.

Is There A Way to Eliminate The APR Bias on a Cash-Out Refinance?


To make it comparable to the APR on a second mortgage, the APR on the cash-out refinance must be converted into a "net-cash APR". A net-cash APR compares the difference in payments between the old and new loan to the amount of cash received by the borrower. It thus takes account of the difference in rate between the old mortgage and the new one.

But this will not happen anytime soon. Meanwhile, the best way to avoid going astray is to use calculator 3d (Cash-Out Refi Vs Second Mortgage). The calculator compares all the costs over a future period of the existing loan plus a second with the costs of the new cash-out refi. It also shows the "break even" rate on the second, which is the highest rate you can pay on the second and come out ahead of the cash-out refi.

Why Should the APR on a High-Rate/Negative Point Loan Be Ignored?


Because there is no clear rule regarding the treatment of negative points in the APR calculation. Different lenders do it in different ways, which means that their APRs are not comparable.

When borrowers pay positive points and/or other fees, which is the usual case, every lender calculates the APR in the same way. The APRs in such cases are always higher than the rates. But on high-rate loans on which lenders pay rebates that cover some or all of the third party fees, there is no consensus on how to calculate the APR. It should but may not be below the interest rate.

On June 9, 2006 I checked this at 4 on-line lenders who quote prices for high rate loans: Amerisave, Eloan, AMRO and IndyMac. Only Amerisave included the full rebate in the calculation, as I would, resulting in an APR significantly below the rate. IndyMac used only a small amount of the rebate in the calculation, so the APR was only slightly below the rate. Eloan and AMRO didn’t use any of the rebate, so their APRs were higher than the rate.

An implication of this is that the APR stated for a "no-cost" mortgage where the lender pays all the settlement costs can be misleadingly high. But borrowers shopping for no-cost mortgages don’t need an ARP, they can shop for the lowest rate.

Other borrowers who need a rebate should shop for the largest rebate at a specified rate. For example, I shopped the 4 lenders mentioned earlier at 7.25% on a 30-year FRM of $400,000, and found rebates ranging from $10,133 to $4300.

Why Is the APR on a HELOC Not Useful?


Because the APR on a HELOC is the initial interest rate, which the borrower already knows.

A HELOC is a line of credit, as opposed to a loan for a specified sum, and it is always adjustable rate. The interest rate on all HELOCs is equal to the prime rate plus a margin, and the rate adjusts the first day of the month following a change in the prime rate. If the HELOC has an introductory guaranteed rate, any rate adjustments are deferred, but typically guaranteed rates hold for only a few months.

The critical price variable is the margin, but that is not a required disclosure. The APR is a required disclosure, but it is defined as the interest rate, which can be well below the prime rate plus the margin. That makes it a useless redundancy. Borrowers shopping for a HELOC should ask for the margin.

Why Is The APR On An ARM A Useful Measure For Borrowers With Long Time Horizons?


Because the APR calculation on an ARM takes account of important ARM features that the borrower often doesn’t know or understand.

The APR calculation on an ARM uses the initial rate for as long as it lasts, and then uses the current value of the rate index used by the ARM, plus the margin, subject to any rate adjustment caps. It is assumed that rate index used by the ARM stays the same for the life of the loan. This is called a "no-change" or "stable- rate" scenario.

Here is an illustration from June, 2006. A 7/1 ARM that uses as its index 1-year Libor had an initial rate of 6.25% with zero points. The value of the index at that time was 5.426% and the margin was 2.25%, summing to 7.676%. The APR is 6.912%, based on 6.25% for 7 years, and 7.676% for the remaining 23. The rate adjustment cap of 5% did not figure in the calculation because the rate increase was smaller.

The APR on an ARM thus takes account of the initial rate and period, the current value of the rate index, the margin, and rate caps. Borrowers often don’t have this information, or don’t know what to do with it if they do have it. This makes the APR on an ARM a useful piece of information, provided that the borrower intends to have the mortgage at least 7 years, and that the ARM is not a HELOC.

But there is one proviso. The APR on an ARM assumes that the rate index stays at the initial level through the entire life of the loan. In general, this is the single best assumption you can make, since no one can predict interest rates years in advance. However, when interest rates are as low as they have ever been, as in 2003-2004, there is much more scope for a future increase than decrease. There is a limit on how low rates can go, but no limit on how high they can go. Under these circumstances, I would be hesitant about comparing the APR on an ARM with that on a FRM.

When Is The APR Locked?


With some lenders, immediately, with others, not until closing.

A lock typically covers the rate and points, but not fixed-dollar fees charged by the lender. Since fixed-dollar fees are a component of the APR, a lender who does not include fixed-dollar fees in its lock can raise them, along with the APR, anytime before closing. A new Truth in Lending statement must be issued each time, but that does not help the borrower nor deter the lender. A lender who delays final approval of the loan until closing can do the same. The Good Faith Estimate that became effective January 1, 2010 eliminated the ability of lenders to raise fixed-dollar fees after a GFE was issued, but delaying loan approval remained an open possibility.

This potential for abuse could be fixed simply by ruling that a lender locking the price also locks the APR. See Why Isn’t the APR Locked With the Rate?

Borrowers avoid the problem if they deal with a mortgage broker, because brokers won’t tolerate a scam that puts money only in the lender’s pocket. See How Much Protection Does a Mortgage Broker Provide? Borrowers can also avoid the problem by only dealing with lenders who guarantee their fees and show them on their web sites.

Can I Calculate the APR Myself?


On a fixed-rate mortgage, it can be done with an inexpensive hand calculator, such as the HP 10B.

Assume the loan amount is $100,000, term 360 months, rate 6%, and APR fees $2,000. The last consists of all lender charges, but not charges for appraisal, credit or other third party services.

1. Enter: -100000 in PV, 360 in N, 6 in I/Yr and 0 in FV.

2. Solve for PMT = 599.5505.

3. Round PMT up to 599.56, enter this number in PMT.

4. Enter loan amount less APR fees in PV as -98000.

5. Solve for I/Yr = 6.190. This is the APR.

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