Loan Amortization on the TI BAII Plus Pro

In this tutorial we will see how to amortize a fixed-rate loan using the TI BAII Plus Professional calculator from Texas Instruments. Specifically, we will see how to calculate the amount of principal and interest for any particular payment, or range of payments. For example, you may wish to know how much your principal or interest payments will be for the first (or any other) year of the loan. If you prefer to use a spreadsheet, which I do, please see my spreadsheet amortization tutorial.

Fully amortizing loans are quite common. Examples include home mortgages, car loans, etc. Typically, but not always, a fully amortizing loan is one that calls for equal payments (annuity) throughout the life of the loan. The loan balance is fully retired after the last payment is made. Each payment on this type of loan consists of interest and principal payments. It is the presence of the principal payment that slowly reduces the loan balance, eventually to \$0.

An amortization schedule is a table that shows each loan payment and a breakdown of the amount of interest and principal paid. Typically, it will also show the remaining balance after each payment has been made.

Calculating Interest and Principal for a Single Payment

Let’s start by reviewing the basics with an example loan that matches the one used in the spreadsheet amortization tutorial:

Imagine that you are about to take out a 30-year fixed-rate mortgage. The terms of the loan specify an initial principal balance (the amount borrowed) of $200,000 and an APR of 6.75%. Payments will be made monthly. What will the monthly payment be? How much of the first payment will be interest, and how much will be principal?

Our first priority is to calculate the monthly payment amount. We can do this most easily by using the TVM keys, and this is required to use the AMORT menu. Be sure to set P/Y to 1 period per year and then enter 30 × 12 into N, 6.75 ÷ 12 into I/Y, 200,000 +|- into PV, and then 0 into FV (just to clear it out). Press CPT PMT to calculate the monthly payment amount and you should find that the payment is \$1,297.20 per month. (Note that your actual mortgage payment would be higher because it would likely include insurance and property tax payments that would be funneled into an escrow account by the mortgage service company.)

That answers our first question. So, we now need to separate that payment into its interest and principal components. We can do this using a couple of simple formulas (we will use some built-in functions in a moment):

$$\text{Monthly Interest Payment} = \text{Principal Balance} \times \text{Monthly Interest Rate}$$

$$\text{Monthly Principal Payment} = \text{Monthly Payment}\,-\, \text{Monthly Interest Payment}$$

Using these formulas, we can see that the interest component of the first payment would be:

$$\text{Interest in 1st Payment} = \text{200,000} \times \text{0.005625} = \text{\$1,125}$$

and the principal payment is:

$$\text{Principal in 1st Payment} = \text{1,297.20} \,- \text{1,125} = \text{\$172.20}$$

Note that the sum of the interest and principal is the amount of the total payment:

$$\text{1,125} + \text{172.20} = \text{\$1,297.20}$$

That is the case for every single payment over the life of the loan. However, as payments are made the loan balance will decline. This, in turn, means that the interest payment will be lower, and the principal payment will be higher (because the total payment amount is constant), for each successive payment.

Using the Built-in Functions

We’ve now seen how the principal and interest components of each payment are calculated. However, you can use a couple of built-in functions to do the math for you. These functions also make it easier to calculate the principal and/or interest for any arbitrary payment. Before we can use these functions, you must enter the loan details into the TVM keys as we did above.

The three functions that we are going to use are the BAL, PRN, and INT functions in the AMORT menu. These functions calculate the remaining balance after the payments are made, and the total amount of interest or principal paid between any two payments. The period for which they are calculated depends on the values specified for P1 and P2 (the beginning and end of the range, respectively).

For example, we can calculate the remaining balance after the first payment by pressing 2nd PV to get into the AMORT menu, and then 1 ENTER for P1, 🠋 1 ENTER for P2, and then 🠋 to find that the remaining balance is 199,827.80. To find the amount of the principal payment in the first payment simply press 🠋 to see that it is 172.20. Press 🠋 again to see that the amount of interest in the first payment is 1,125.00.

Those answers match exactly the ones that we calculated manually above. If we were interested instead in, say, payment 28, then we would simply enter 28 into both P1 and P2. You can use 🠋 or 🠉 to move through the AMORT menu and change the inputs. If you do change those, you will find that after the 28th payment the remaining balance is 194,793.88. Further, the principal part of the 28th payment would be 200.35, and the interest part would be 1,096.84. (the principal and interest components sum to 1,297.20, except for slight rounding).

We can also use these functions to calculate the interest and principal for any range of periods by specifying that P1 and P2 are different. So, we can calculate the total amount of principal and interest payments in the first year by setting P1 to 1 and P2 to 12. Use the 🠋 key to find that the total principal reduction in the first year is 2,131.50, and the total interest paid is 13,434.86.

To do the same thing for the last year, we would set P1 to 349 and P2 to 360. In the last year, the total principal paid is 15,011.84, and the total interest is 554.51. Finally, the remaining balance at the end of the loan is -0.0034 (really, it is exactly 0).

Creating an Amortization Schedule

As noted in the beginning, an amortization schedule is simply a listing of each payment and the breakdown of interest, principal, and remaining balance. For this loan, an amortization table for the first six months would look like this from my spreadsheet amortization schedule:

If you haven’t been following along, you will first need to enter the loan data (as shown above) into the TVM keys before you can create an amortization schedule. Then, you would need to go period by period, each time resetting both P1 and P2 and writing down the results. Obviously, this is hilariously impractical. Still, you could do it. Much better, though, to use a more appropriate tool such as a spreadsheet or a dedicated program. Nonetheless, the AMORT feature of the TI BAII Plus Professional calculator may be useful once in a while.

I hope that you have found this tutorial to be helpful.