# APR Calculations

#### Example One – Two loans with the same interest rate but different closing costs:

Both loans are 30 year \$200,000, 4.5% fixed interest rate with a monthly payment for principal and interest of \$1,013.37.  (I will demonstrate how to calculate the APR below.) Loan one has closing costs of \$5,745 and thus a calculated APR of 4.75%. You would make a payment based on 4.5%, but the APR of 4.75% gives you a way of viewing the loan including the closing costs affiliated with that particular loan.

The second loan has the same note rate of 4.5%, monthly mortgage payment of \$1,013.37, but closing costs of \$9,050 resulting in an APR of 4.90%.

When the loans have the same interest rate and monthly payment the decision is pretty easy.  Choose the one with the lower closing costs. Why?  The note rate, and thus the mortgage payment, is the same for both but the second loan had higher upfront closing costs, as evidenced by the APR, and thus more expensive over time.

Here is how the APRs would be calculated for this example.  The process to compute the APR starts by subtracting the loan costs from the loan amount because what youâ€™re paying to get the loan (the closing costs) effectively reduces what you have borrowed.  In our example for a loan of \$200,000 with closing costs of \$5,745, the real amount you will be borrowing is the difference, \$194,255.

You will need a mortgage calculator that allows you to change all the parameters in order to continue with the process.  Most mortgage calculators aren’t setup to do this.  Most mortgage calculators simply compute the mortgage payment but won’t allow you to enter a specific mortgage payment and work backwards.  I found a mortgage calculator that works in the Apple App Store called “RECalc”.  I think you will find it useful not only for these calculations but also for other mortgage calculations including a function that summarizes the loan as well as shows the amortization schedule.  You will also find “instructions” on using the app in the settings.  Download it and continue.

Let’s test our use of the RECalc app by first verifying the monthly mortgage amount for a loan of \$200,000, 30 year fixed rate at 4.5%.  Using the RECalc app, start by hitting the settings button in the upper left corner.  Go to the section mid page that says, “ENTER TERM IN” and check “Years”.  Then hit the “done” button in the upper right corner to go back to the home page.

Now hit the Red “AC” button to clear the app.  Next enter 200000 and hit the “Amt” button.  Then enter 30 and hit the “Term” button.  Then enter 4.5 and hit the “Int” button.  Then hit the “Pmt” button and then the Orange “=” button and the monthly payment of \$1,013.37 should appear.  Make sure that you end up with the same amount for the monthly payment.  We are then ready to proceed further with our calculations.

Calculating the APR for loan one.  Hit the Red “C” or “AC” button, depending on which is showing, to clear the app.  Then we enter 194255 (\$200,000 loan amount less the closing costs of \$5,745 = net amount of \$194,255) and hit the “Amt” button.  Then enter 30 and hit the “Term” button.  Then enter 1013.37 and hit the “Pmt” button.  Now hit the “Int” button and then the Orange “=” button and the amount showing should be the APR for the first loan of 4.75%.

In other words, it took into consideration the closing costs by deducting them and then recalculating what the interest rate would be for the lower loan amount but with the same monthly payment.

Now let’s look at loan two with closing costs of \$9,050.  Hit the Red “C” or “AC” button, depending on which is showing, to clear the app.  Then we enter 190950 (\$200,000 loan amount less the closing costs of \$9,050 = net amount of \$190,950) and hit the “Amt” button.  Then enter 30 and hit the “Term” button.  Then enter 1013.37 and hit the “Pmt” button.  Now hit the “Int” button and then the Orange “=” button and the amount showing should be the APR for the second loan of 4.90%.

#### Example Two – Two loans with different interest rates and different closing costs.

Here things get more complicated.  However, the APR calculation is most useful in the case of two loans with different interest rates and closing costs.  Loan one may have a lower interest rate and lower mortgage payment, but could have higher closing costs than loan two.  As a result loan two with the higher interest rate and mortgage payment might be the better loan if its APR calculation is lower.

Let’s go back to our previous example.  Let’s use the \$200,000 loan at 4.5% over 30 years with the \$9,050 closing costs for loan one.  And, for loan two, \$200,000 loan at 4.6% over 30 years with \$3,500 closing costs.

Loan one has a monthly loan payment of \$1,013.37 just as our first example.  Loan two, \$200,000 at 4.6% over 30 years has a monthly loan payment of \$1,025.29.

Let’s calculate the APR for loan one.  The loan amount is \$190,950 (\$200,000 less the closing costs of \$9,050 = \$190,950).  Hit the Red “C” or “AC” button, depending on which is showing, to clear the app.  Enter 190950 and hit the “Amt” button.  Then enter 30 and hit the “Term” button.  Next enter 1013.37 and hit the “Pmt” button.  Then hit the “Int” slot and then the Orange “=” sign to arrive at the APR of 4.9%.

Let’s calculate the APR for loan two.  The loan amount is \$196,500 (\$200,000 less the closing costs of \$3,500 = \$196,500).  Hit the Red “C” or “AC” button, depending on which is showing, to clear the app.  Then enter 196500 and hit the “Amt” button.  Then enter 30 and hit the “Term” button.  Next enter 1025.29 and hit the “Pmt” button.  Then hit the “Int” button and then the Orange “=” sign to arrive at the APR of 4.752%.

Comparing the two calculations it appears that the second loan with the higher interest rate is the better of the two loans based on their APRs.