Loan Amortization on the HP 17BII

In this tutorial we will see how to amortize a fixed-rate loan using the HP 17BII calculator from Hewlett Packard. 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/YR to 1 period per year (from the TVM menu, press OTHER then 1 P/YR) and then enter 30 × 12 into N, 6.75 ÷ 12 into I%YR, 200,000 +/- into PV, and then 0 into FV (just to clear it out). Press 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, PRIN, and INT functions in the AMRT 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, or range of periods, for which they are calculated depends on the values specified for #P. If you enter 1 into #P, then it will do one payment at a time. If you enter 12, it will do one year at a time. And so on.

For example, we can calculate the remaining balance after the first payment by pressing OTHER and then the AMRT menu item to get into the menu, and then 1 #P for the number of payments to include. Next, press BAL to find that the remaining balance is 199,827.80. To find the amount of the principal payment in the first payment simply press PRIN to see that it is 172.20. Press INT 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 need to cheat a little bit. Press EXIT and then AMRT to reset the amortization. Next, press 27 #P (note that this is one payment before the one that we want) and then 1 #P. This will cause it to calculate the 28th payment, and you will see PMTS: 28-28 on the screen. If you do that, 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). As noted above, you could also repeatedly press NEXT until you get to payment 28.

We can also use these functions to calculate the interest and principal for any range of periods by specifying #P. Press EXIT and then AMRT to reset the amortization. We can calculate the total amount of principal and interest payments in the first year by setting #P to 12. Use the BAL, PRIN, and INT keys to find that the loan balance after the first year is 197,868.50, the total principal reduction in the first year is 2,131.50, and the total interest paid is 13,434.86. If you press NEXT, you can calculate the values for the second year.

To do the same thing for the last year, we would set #P to 348 (again, this is one payment before the starting payment) and then set it again to 12. You should see PMTS: 349-360 on the screen. 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, by pressing NEXT repeatedly, 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 HP 17BII calculator may be useful once in a while.

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