INTEREST
The type of interest that is most commonly calculated on short-term loans is simple
interest. Simple interest is calculated only on the original principal amount and is paid at the end
of the loan period. Interest is the fee or rent that lenders charge to borrowers for the temporary
used of borrowed money. The amount borrowed is called principal. The rate of interest is the
percentage of the principal that will be charge for the specified period of time (e.g daily, weekly,
monthly, and yearly, etc.).
The following variables will be in our mathematical treatment of simple interest;
P=Principal amount of the loan investment
r=Annual rate of simple interest
t=Time period (term) of the loan or investment
I=Amount of interest paid or received
F=Maturity value of the loan or investment
Simple Interest Formula:
I=Prt P=I/rt F=P+I F=P(1+rt)
A. Determining the Time Period
To find the due date, we must determine the number of days in each month. Then, we simply
compute month by month, the number of days from one date to another.
The loan date is the first day of loan and due date (or maturity date) is the loan. When these two
dates are known, the number of days of the loan can calculated by using the days in each month
as reflected in table.
The Number of Days in Each Month
Month No. of Days Month No. of Days
January 31 July 31
February 28 August 31
March 31 September 30
April 30 October 31
May 31 November 30
June 30 December 31
B. Actual and Approximate Time
The time period should be determined using the number of days involved. There are two
ways of determining the time period. It may be approximate or actual time. Approximate time
uses 30 days in every month, while the actual time uses the exact number of days in every
specific month as shown in table.
, Example 1. Determine the actual time and approximate time from March 3, 2015 to September
10, 2015.
Solution:
Month Actual Time Approximate Time
March 3,2015 31-3=28 30-3=27
April 30 30
May 31 30
June 30 30
July 31 30
August 31 30
September 10, 2015 10 10
Total 191 187
There are 191 days in actual time, while 187 days in approximate time.
Example 2. Find the actual and approximate time from November 18, 2015 to May 9, 2016.
Solution:
Since 2016 is leap year, the month of February contains 29 days in the actual time. Thus, the
solution will be
Month Actual Time Approximate Time
November 18, 2015 30-18=12 30-18=12
December 31 30
January 31 30
February 29 30
March 31 30
April 30 30
May 9, 2016 9 9
Total 173 171
There are 173 days in actual time, while 171 days in approximate time.
C. Exact interest is computed in a 365 days in a year as the time factor denominator. On the
other hand, ordinary interest is a type of interest wherein the number of days is computed
based on 360 days in a year. Banks and most other institution still use ordinary interest
because it yields a somewhat higher as compared to exact interest method. If the type of
interest is not specified in any problem, the problem will be solved using Banker’s Rule
or Ordinary interest in actual time.
Number of days of a loan
Ordinary Interest :Time=
360
The type of interest that is most commonly calculated on short-term loans is simple
interest. Simple interest is calculated only on the original principal amount and is paid at the end
of the loan period. Interest is the fee or rent that lenders charge to borrowers for the temporary
used of borrowed money. The amount borrowed is called principal. The rate of interest is the
percentage of the principal that will be charge for the specified period of time (e.g daily, weekly,
monthly, and yearly, etc.).
The following variables will be in our mathematical treatment of simple interest;
P=Principal amount of the loan investment
r=Annual rate of simple interest
t=Time period (term) of the loan or investment
I=Amount of interest paid or received
F=Maturity value of the loan or investment
Simple Interest Formula:
I=Prt P=I/rt F=P+I F=P(1+rt)
A. Determining the Time Period
To find the due date, we must determine the number of days in each month. Then, we simply
compute month by month, the number of days from one date to another.
The loan date is the first day of loan and due date (or maturity date) is the loan. When these two
dates are known, the number of days of the loan can calculated by using the days in each month
as reflected in table.
The Number of Days in Each Month
Month No. of Days Month No. of Days
January 31 July 31
February 28 August 31
March 31 September 30
April 30 October 31
May 31 November 30
June 30 December 31
B. Actual and Approximate Time
The time period should be determined using the number of days involved. There are two
ways of determining the time period. It may be approximate or actual time. Approximate time
uses 30 days in every month, while the actual time uses the exact number of days in every
specific month as shown in table.
, Example 1. Determine the actual time and approximate time from March 3, 2015 to September
10, 2015.
Solution:
Month Actual Time Approximate Time
March 3,2015 31-3=28 30-3=27
April 30 30
May 31 30
June 30 30
July 31 30
August 31 30
September 10, 2015 10 10
Total 191 187
There are 191 days in actual time, while 187 days in approximate time.
Example 2. Find the actual and approximate time from November 18, 2015 to May 9, 2016.
Solution:
Since 2016 is leap year, the month of February contains 29 days in the actual time. Thus, the
solution will be
Month Actual Time Approximate Time
November 18, 2015 30-18=12 30-18=12
December 31 30
January 31 30
February 29 30
March 31 30
April 30 30
May 9, 2016 9 9
Total 173 171
There are 173 days in actual time, while 171 days in approximate time.
C. Exact interest is computed in a 365 days in a year as the time factor denominator. On the
other hand, ordinary interest is a type of interest wherein the number of days is computed
based on 360 days in a year. Banks and most other institution still use ordinary interest
because it yields a somewhat higher as compared to exact interest method. If the type of
interest is not specified in any problem, the problem will be solved using Banker’s Rule
or Ordinary interest in actual time.
Number of days of a loan
Ordinary Interest :Time=
360
