The Art of Mathematics in Business. Dr Jae K Shim
date while other loans state the period of the loan in days or months. When the maturity date is given in days, the date is determined by counting the days from the day the loan was secured. The day on which the loan is procured is not counted. For example, a 120-day loan obtained on October 17, 20×7, is due on February 15, 20×8. When the period is given in months, the loan’s maturity date falls on the same day of the month as the date the loan is issued. For example a 6-month loan dated March 15 matures on September 15. If the due date of the loan falls on a nonbusiness day, the maturity date is the next business day, with an additional day(s) added to the period for which interest is charged.
Example
Motor Parts, Inc., obtained a 90-day loan dated March 16, 20×7. The maturity date of the loan is June 15, 20×7, as determined below.
To determine the maturity date, calculate forward for the exact number of days in the loan period. Do not count the day on which you actually received the loan. Remember that some months have 30 days and some have 31.
How is it used and applied?
Due dates are not approximations; they are precise and final. On that date, you must be prepared to make full payment. Failure to do so means that you have defaulted on a loan and that can have disastrous consequences for your business.
It is critical, therefore, that you know the exact date well in advance so you can make certain you will have the funds available.
5. Promissory Notes and Bank Discounts
Introduction
A business may both make a promissory note and receive one. Notes receivable and notes payable are formal arrangements promising payment. Often a debtor signs a promissory note, which serves as evidence of a debt. The promissory note is a written promise to pay principal with interest at a maturity date. A business owner might discount a note if cash is needed quickly and he or she does not wish to hold the note until its maturity date.
How is it computed?
As with loans, some notes specify the maturity date, while others state the period of the note, in days or months. When the maturity value is given in days, the maturity date is determined by counting the days from issue. Interest is usually computed on the basis of a 360-day year (12 months × 30 days per month.) Recall from Sec. 1 that the following formula is used:
Interest = principal × interest rate × time
For example, the maturity date of a 90-day note issued May 6, 20×8, is August 4, 20×8, computed as follows:
When the period is given in months, the note’s maturity date falls on the same day of the month as the date of the note is issued. For example a 6-month note dated January 15 matures on July 15. If the due date of the note falls on a nonbusiness day, the maturity date is the next business day, with the additional day(s) added to the period for which interest is charged.
If you are holding a promissory note from a supplier or other party, you may find yourself in the position of needing more money before the due date, in which case you may discount the note receivable at a bank or finance company.
The proceeds received by the holder at the time the note is discounted are equal to the maturity value less the bank discount (interest charge). The bank discount is based on the period of time the bank will hold the note and the note’s interest rate. The interest rate charged by the bank need not be the same as the interest rate on the marker’s note. In fact, it is usually higher, because the bank generally charges a higher interest rate. The rate may also be different because of changes in the going interest rate since the note was originally written. The maturity value of the note is found as follows:
Maturity value = face value of note + interest income
The bank discount is:
Bank discount = maturity value × bank discount × period of time held by bank
Example 1
On June 30, 20××, Susan Ray, a business owner, issued a 180-day, 18 percent note to the Denmark Company to pay a short-term business loan. The note’s interest rate 6 months later will be $900, calculated as follows:
Principal × rate of interest × time = interest
$10,000 × 18% × 6 months = $900
Example 2
The Solvay Tool Company received the following notes:
The due date and amount of interest on each note is:
| Due Date | Interest Rate (%) | Face Amount |
| (a) Nov. 30 | $ 20 ($1,000 × 4/12 × 6%) | $1,020.00 |
| (b) Oct. 10 | 100 ($7,500 × 60/360 × 8%) | 7,600.00 |
| (c) Oct. 24 | 22.50 ($7,200 × 45/360 × 9%) | 2,022.50 |
| (d) Aug. 18 | 150 ($5,000 × 90/360 × 12%) | 5,150.00 |
Example 3
On June 20, 20×8, the Bunyan Grass Seed Company received a 90-day, 12 percent note receivable for $5,000. On August 5 the company, in need of cash, discounts the note at its bank. The bank charges a discount rate of 15 percent. The proceeds from the discounted note are 5,077.04 calculated as follows:
Bank discount = maturity value × discount rate × period note is held by bank
| Face value of note dated June 20 | $5,000.00 |
| Add: Interest on note ($5,000 × 12% × 90/360) | $150.00 |
| Maturity value of note due Sept. 18 | $5,150.00 |
| Bank discount on maturity value ($5,000 × 12% × 90/360) | $72.96 |
The net proceeds received by the payee at the time of discounting are:
Net proceeds = maturity value - bank discount
| Maturity value of note dated Sept. 18 | $5,150.00 |
| Less: Discount period (Aug. 5 – Sept. 18 = 34 days) | |
| Discount on maturity value (34 days at I5%) | $72.96 |
| Net proceeds of note after discounting | $5,077.04 |
How is it used and applied?
When a note receivable is sold or discounted to a bank or other financial institution, the seller (business owner) of the note remains contingently liable until the maker pays at maturity. If the original maker of the note does not pay the note at its maturity, the bank will seek payment from the seller of the note. The party who originally discounted the note will not be forced to pay and must seek reimbursement from the original maker of the note.
1.6 Trade Credit
Introduction
When you buy supplies or materials on credit, you are agreeing to pay the supplier within a certain period after receiving the goods. This is called trade credit, because it is a sale within the trade (as opposed to a sale to the public at large), and it is in effect a form of loan: you get the materials now and pay for them later. Many suppliers also offer a discount if you pay early.
How is it computed?
Trade credit is usually extended for a specific period of time; 30 days is common. This means that payment is due 30 days after you receive the merchandise. If a supplier offers a discount, there is also a specific period during which the discount may be taken. One very common arrangement is 2/10, net 30, sometimes written 2/10, n/30, which means that if you pay the invoice within 10 days, you can take a 2 percent discount; otherwise, the full amount is due within 30 days. The cost of not taking the discount is referred to as the opportunity cost of credit; it can be substantial.
The cost of credit if a cash