 # Long-Term Obligations

## Long-Term Notes

The previous chapter illustrations of notes were based on the assumption that the notes were of fairly short duration. Now, let's turn our attention to longer term notes. A borrower may desire a longer term for their loan. It would not be uncommon to find two, three, five-year, and even longer term notes. These notes may evidence a "term loan," where "interest only" is paid during the period of borrowing and the balance of the note is due at maturity. The entries are virtually the same as you saw in the previous chapter. As a refresher, assume that Wilson issued a five-year, 8% term note -with interest paid annually on September 30 of each year:

 10-1-x3 Cash 10,000 Note Payable 10,000 To record note payable at 8% per annum; maturity date on 9-30-X8 12-31-xx Interest Expense 200 Interest Payable 200 To record accrued interest for 3 months (\$10,000 X 8% X 3/12) at end of each year 9-30-xx Interest Expense 600 Interest Payable 200 Cash 800 To record interest payment (\$10,000 X 8% = \$800, of which \$200 was previously accrued at the prior year end) each September 9-30-x8 Interest Expense 600 Interest Payable 200 Note Payable 10,000 Cash 10,800 To record final interest payment and balance of note at maturity

Other notes may require level payments over their terms, so that the interest and principal are fully paid by the end of their term. Such notes are very common. You may be familiar with this type of arrangement if you have financed a car or home. By the way, when you finance real estate, payment of the note is usually secured by the property being financed (if you don't pay, the lender can foreclose on the real estate and take it over). Notes thus secured are called "mortgage notes."

### How do I Compute the Payment on a Note?

With the term note illustrated above, it was fairly easy to see that the interest amounted to \$800 per year, and the full \$10,000 balance was due at maturity. But, what if the goal is to come up with an equal annual payment that will pay all the interest and principal by the time the last payment is made? From my years of teaching, I know that students tend to perk up when this subject is covered. It seems to be a relevant question to many people, as this is the structure typically used for automobile and real estate ("mortgage") financing transactions. So, now you are about to learn how to calculate the correct amount of the payment on such a loan. The first step is to learn about future value and present value calculations.

### Future Value

Let us begin by thinking about how invested money can grow with interest. What will be the future value of an investment? If you invest \$1 for one year, at 10% interest per year, how much will you have at the end of the year? The answer, of course, is \$1.10. This is calculated by multiplying the \$1 by 10% (\$1 X 10% = \$0.10) and adding the \$0.10 to the dollar you started with. And, if the resulting \$1.10 is invested for another year at 10%, how much will you have? The answer is \$1.21. That is, \$1.10 X 10% = \$0.11, which is added to the \$1.10 you started with. This process will continue, year after year. The annual interest each year is larger than the year before because of "compounding." Compounding simply means that your investment is growing with accumulated interest, and you are earning interest on previously accrued interest that becomes part of your total investment pool. In contrast to "compound interest" is "simple interest" that does not provide for compounding, such that \$1 invested for two years at 10% would only grow to \$1.20. Not to belabor the mathematics of the above observation, but you should note the following formula:

Where "i" is the interest rate per period and "n" is the number of periods

The formula will reveal how much an investment of \$1 will grow to after "n" periods. For example, (1.10)2 = 1.21. Or, if \$1 was invested for 5 years at 6%, then it would grow to about \$1.34 ((1.06)5 = 1.33823). Of course, if \$1,000 was invested for 5 years at 6%, it would grow to \$1,338.23; this is determined by multiplying the derived factor times the amount invested at the beginning of the 5-year period. Hopefully, you will see that it is not a great challenge to figure out how much an up-front lump sum investment can grow to become after a given number of periods at a stated interest rate. This calculation is aptly termed the "future value of a lump sum amount." Future Value Tables are available that include precalculated values (the tables are found in the Appendix to this book). See if you can find the 1.33823 factor in a future value table. Likewise, use the table to determine that \$5,000, invested for 10 years, at 4%, will grow to \$7,401.20 (\$5,000 X 1.48024).