Business Mathematics: Interest and Discount - Methods For Computing Simple Interest

There are four distinct methods for computing simple interest between two dates:
1. Exact time and ordinary interest
2. Exact time and exact interest
3. Approximate time and ordinary interest
4. Approximate time and exact interest

Method 1 is also known as the “banker’s rule” and is the common method used in business in the United States and in international business transactions.

Method 2 is used by the U.S. government.

Method 3 is used for periodic repayment plans, such as monthly payments on real estate mortgages, installment purchases, and certain types of personal borrowing, and in computing accrued bond interest on corporate bonds.

Method 4 is theoretically possible but never used.

Example
A sum of $75,000 is invested from March 13 until December 20 of the same year at 15½% simple interest.

For each of the four methods, the interest earned is illustrated below.

(a)  Exact time and ordinary interest:

The calculation to find the exact time is as follows:

To find t for ordinary interest, we have to use a year based on 360 days:

We can now calculate the interest:

(b)  Exact time and exact interest:
From (a) we know the exact number of days is 282. To find t for exact interest, we have to use a 365-day year:

 

(c)  Approximate time and ordinary interest:
To find approximate time, we construct a table and subtract:

We then convert to approximate time in days:
(9 mo × 30 days/mo) + 7 days = 277 days

For ordinary interest we use a 360-day year to calculate t:

(d) Approximate time and exact interest:

From (c) we know that the number of approximate days is 277. Using a 365-day year to calculate t, we get


Solved Problems:

5.17 A sum of $2,000 is invested from April 9 to December 3 of the same year at 15% simple interest. Find the interest earned using the four methods.
 

Solution
From Prob. 5.9 the exact time is 238 days, and from Prob. 5.12 the approximate time is 234 days.


5.18 Using the banker’s rule, find the simple interest on $1,800 at 17¼% from February 4 to April 21 of the same leap year.
 

Solution
From Prob. 5.10 the exact time is 77 days:


5.19 Find the maturity value (see Sec. 5.1) of a note for $1,500 at 12% ordinary simple interest for 182 days.
 

Solution


5.20 Joe borrowed $1,200 on September 10 to start college. He repaid the loan on July 20 of the following year. What amount did he pay back if the bank calculated the exact interest at 11% and used the exact time?
 

Solution
Exact time from September 10 to July 20 of the following year:

Interest paid:

To determine how much Joe paid back, we calculate the maturity value of the loan.

Joe paid the bank $1,313.19.