Business Math - Simple Interest

clock, book, and paper with background of numbers

Simple Interest

Home / Lessons - Exam 3 / All Lessons / Assignments / Sample Exam / Sample Exam with Answers

Objective: To develop an understanding of simple interest as an application of the basic percentage formula P = R ^. B and, an understanding of simple interest as an example of the inverse process where the basic formula B_I = B(1 + R_I) is applicable.

Background: Most financial considerations can be classified in one of two categories: loans (debt), or, investments. Each of these two considerations are fundamentally based on an interest rate which is a rate of increase for a specific period of time (the process is an increase process). The effect on consumers is either interest income for an investment, or, interest expense for a loan. These interest categories were utilized previously in the income tax consideration.

Interest calculations, whether for a loan or an investment, are exactly the same. Interest calculations can be either in simple interest or compound interest. For simple interest, the principal only earns interest. For compound interest, both the principal, as well as previously earned interest, earn interest. The difference in these two types is dramatic. The current consideration is simple interest. Compound interest will be considered later.

Reading Assignment: As per syllabus

Definitions:

Interest - is money paid for the use of money. I will be the symbol used to denote interest.

Principal is the amount of money borrowed or invested. P will be the symbol used to denote principal.

Interest rate (simple) - is the rate, or percent, stated on an annual (or yearly) basis. r will be the symbol to denote the simple interest rate.

Maturity value or accumulated value, denoted with A, is the increased amount resulting from the increase process. The maturity, value A, is obviously the sum of principal, P, plus interest, I.

Time, An Additional Factor: Money borrowed or invested will always be for some period of time. Since interest rates are expressed on an annual basis, some appropriate multiple, or fractional representation, of time must be used. This is denoted by t.

Transformation of Statement of Time to t: The standard measure of time for simple interest is either in years, months, or days, Each must be transformed into an appropriate t:

Time	t
n years	n
n months
n days	, Exact Interest , Ordinary Interest

If time is given in days, ordinary or exact interest must be specified. Examples that follow will illustrate these concepts and methods.

Simple Interest as an Application of P = R

P (Percentage)	=	R (Rate or Percent)	(B (Base

I (Interest)	=	r (Simple Interest rate)t	P (Principal)

R = rt since the rate is applied multiple, or fractional, times.

Simple Interest as an Application of B_I = B(1 + R_I)

B_I(Increased Base)	=	B (Base)	(1 + R_I) (Accumulation factor)

A (Maturity Value)	=	P (Principal)	(1 + rt) (Accumulation factor)

Basic Formulas:

I = Prt

(P = R B)

Interest equals principal times rate times representation of time.

A = P + I

(B_I= B + R_IB)

Accumulated value, or, equals Principal plus Interest Maturity Value

then,

A = P + Prt = P(1+rt)

(B_I = B(1 + R_I))

Of course, these variations of the basic formulas are also valid and useful.

P =

t =

r =

P =

See the sample exam for examples and applications as well as the examples in the text. Examples that follow are provided to clarify use of the formulas, transformation of statement of time to an appropriate t, and proper procedures.

Example 1: Find interest on $1000 at 6% simple interest for 3 years.
I = Prt Time = 3 years; t = 3
*I = 1000 .06 * 3** This Multiplication gives the interest for 1 year since 6% is given on a yearly basis. I = 180		This is appropriate since the increase process of 6% per year is repeated for 3 years, or a multiple of 3 is needed.

Example 2: Find interest on $1000 at 6% simple interest for 6 months.

I = Prt

I = 1000 * .06 *

Time = 6 months; t =

This multiplication gives the interest for 1 year since 6% is given on a yearly basis.
I = 30

This is an appropriate multiple since
1000 * .06 gives the yearly amount. The time was 6 months or one-half of a year.

Example 3: Find interest on $1000 at 6% exact interest for 60 days

I = Prt

I = 1000 * .06 *

Time = 6o days; t =

This multiplication gives the interest for 1 year since 6% is given on a yearly basis.
I = 9.86

Exact interest

365 days. The fraction gives the appropriate fractional part of one year's interest fo the period of 60 days.

Example 4: Find interest on $1000 at 6% ordinary interest from February 14 to May 30.

When calendar dates are given, consult page 499 in text for table where each day of the year is numbered.

May 30	150
February 14	-45
	105 days

I = Prt

I = 1000 * .06 *

Time = 6o days; t =

This multiplication gives the interest for 1 year since 6% is given on a yearly basis.
I = 15.50

Ordinary interest

360 days. The fraction

gives the appropriate fractional part of one year's interest for the time period of 105 days.

Example 5: Find the maturity value of $1000 at 8% ordinary interest from June 1 to August 31.

August 31	243	Use Table on page 499 to find the number of the days of the year for each date.
June 1	-152
	91 days

I = P(1 + rt)

I = 1000(1 + .08 *

) = 1020.22

Example 6: Find the principal needed to accumulate to $10,000 at 7% simple interest for 5 years.
A = P(1 + rt)
P =	Note: Reversing the increase process of simple interest - Division by the accumulation factor.
P =
P = 8264.46

The following examples are provided in conjunction with the material in the text related to discounts on purchases when money is borrowed to take advantage of the discount. Please refer to the text material as well as the sample exam for additional information.

Example 7: How much would be saved on an invoice for $1200 with terms 3/15, n/60 if money can be borrowed at 9% ordinary?

discount rate is 3%; assume money is borrowed for 60 - 15 = 45 days

1200 .03 36.00 Discount*

1200 -36 1164 Amount borrowed for 45 days @ 9%
I = Prt
I = 1200 * .09 * (ordinary)
I = 13.50
Savings = Discount - Interest
Savings = 36.00 - 13.50 = 22.50

Example 8: Find the ordinary interest rate at which a buyer could afford to borrow to take advantage of the cash discount for an invoice of $800 with terms 2/20, n/45.

discount rate is 2%; assume money is borrowed for 45 - 20 = 25 days
In order to save money, interest must be less than discount. Assume that interest equals discount.

800
*.02
16.00 Discount

800
-16
784 Amount borrowed for 25 days

I = Prt

r =

= .29388 = 29.39%

If money can be borrowed for less than 29.39%, a savings will occur.

Remark: Consult the textbook for additional examples and supportive information. Additionally, the sample exam will provide additional examples of all the essential concepts and methods.

Simple Interest Summary

Time	t
n years	n
n months
n days	, Exact Interest , Ordinary Interest

I = Prt and variations	P = , r = , t =
A = P + I
A = P(1 + rt)
P =

If calendar dates are given, use page 499 for the table which numbers each day of the year.

Home / Lessons - Exam 3 / All Lessons / Assignments / Sample Exam / Sample Exam with Answers