Business Mathematics: Interest and Discount - Calculating Due Dates

If the term of a loan is given in months, the due date of the loan is a corresponding day in the maturity month.

There are two qualifying conditions:
1. If the maturity month does not have the required number of days, then the last day of the month serves as the maturity date. Thus, a 2-month loan dated December 31 is due on February 28 (or February 29 in a leap year).
2. If the due date of a loan 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.

Example
(a) A 15-month loan dated February 2 is due May 2 of the following year. (b) A loan dated May 31 and due in 4 months has a maturity date of September 30. (c) A 7-month loan dated December 4 is due July 5, since July 4 is a holiday.
Interest is charged for the extra day the loan is outstanding. For simplicity, we have assumed that the maturity dates in (a) and (b) fall on a business day. Should this not be the case, then the due date is postponed until the next business day and interest is charged [just as in (c)].

When the time is given in days, we may calculate either (1) exact simple interest on the basis of a 365-day year (leap year or not) or (2) ordinary simple interest on the basis of a 360-day year, called a banker’s year. Of the two, ordinary interest brings greater revenue to the lender.

The formulas for calculating time (t) for exact and ordinary simple interest are


Example
Find the exact and the ordinary simple interest on a 60-day loan of $1,950 at 13½%.
We know that P = $1,950 and r = 13½% = 0.135, but we must calculate t for each type of interest

The respective simple interests are

There are two ways to calculate the number of days between calendar dates.

1.Exact time is the count of the actual number of days, including all except the first day. Exact time can be easily found from Table 5.1 by subtracting the serial numbers of the given dates. (April 15, for example, has a serial number of 105 since it is the 105th day of the year.) In leap years, serial numbers of all days after February 28 are increased by 1 (so that the serial number for April 15 would be 106).

2.Approximate time is found by assuming that each month has 30 days.

Table: The Number of Each Day of the Year

Note: For leap year add 1 to the tabulated number after February 28.

Example
(a)  Find the exact time from January 18 to July 9 of the same year, when the year is a leap year. From Table 5.1:

(b)  Find the approximate time between January 18 and July 9. To do this, we set up a table and subtract, as shown:

To restate in days the approximate time of 5 months and 21 days, we proceed as follows:
(5 mo × 30 days/mo) + 21 days = 150 days + 21 days = 171 days

Solved Problems

5.6 Find the exact simple interest on a 90-day loan of $900 at 15¼%.
 

Solution


5.7 Find the ordinary simple interest for the loan in Prob. 5.6.
 

Solution


5.8  Find the (a) exact and (b) ordinary simple interest on a 120-day loan of $145,000 that has an annual interest rate of 19¾%. (c) Which gives the lender a greater return on the $145,000 investment and by how much?
 

Solution
(a)  Exact simple interest

(b) Ordinary simple interest

(c) Of the two, ordinary simple interest gives the lender $130.76 more interest on this investment.

5.9 Find the exact time from April 9 to December 3 of the same year.
 

Solution
From Table above:


5.10 Find the exact time from February 4 to April 21 of the same leap year.
 

Solution


5.11 Find the exact time from May 18 to July 5 of the following year.
 

Solution


5.12 Find the approximate time in Prob. 5.9.
 

Solution

The approximate time is 7 months and 24 days, or (7 × 30) + 24 = 234 days.

5.13 Find the approximate time in Prob. 5.11.
 

Solution

The approximate time is 13 months and 17 days, or (13 × 30) + 17 = 407 days.

5.14 Find the maturity date of a 60-day loan dated June 15.
 

Solution


5.15 Find the maturity date on a 120-day loan dated August 1.
 

Solution


5.16 Find the due date on a 3-month loan dated April 4.
 

Solution
Three months after April 4 is July 4, which is a legal holiday. Therefore the due date is July 5 (if a business day), and interest is charged for 91 days if approximate time is used or for 92 days if exact time is used.