49 Business Math _ 123

Business Math
Chapter 11:
Simple Interest and
Simple Discount
1


11.1 The Simple Interest Formula


Find simple interest by using the
simple interest formula.



Find the maturity of a loan.



Convert months to a fractional or
decimal part of the year.



Find the principal, rate or time using
the simple interest formula.
2

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Key Terms


Interest: an amount paid or earned for the
use of money.



Simple interest: interest earned when a
loan or investment is repaid in a lump sum.



Principal: the amount of money borrowed
or invested.



Rate: the percent of the principal paid as
interest per time period.



Time: the number of days, months or
years that the money is borrowed or
invested.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

11.1.1 The Simple Interest Formula


The interest formula shows how
interest, rate, and time are related
and gives us a way of finding one of
these values if the other three values
are known.

I=PxRxT
4
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Find the simple interest using
the simple interest formula

5
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Identify the principal,
rate and time.
P= R x B


The interest is a percentage.



Principal is the amount borrowed or
invested.



Rate of interest is a percent for a given
time period, usually one year.



Time must be expressed in the same
unit of time as the rate. (i.e. one year)
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Find the interest paid on a loan.


Principal = (P) $1,500.



Interest rate = 9% (or 0.09)



Time = 1 year



Interest = P x R x T



Interest = 1,500 x 0.09 x 1



Interest = $135



The interest on the loan is $135.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Try these examples.


Find the interest on a 2-year loan of
$4,000 at a 6% rate.
 $480



Find the interest earned on a 3-year
investment of $5,000 at 4.5%
interest.
 $675
8

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


11.1.2 Find the maturity value
of a loan.


Maturity value: the total amount of
money due by the end of a loan period;
the amount of the loan and interest.



If the principal and the interest are
known, add them.



MV = principal + PRT



MV = P(1+RT)
9

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Look at this example.


Marcus Logan can purchase furniture on a
2-year simple interest loan at 9% interest
per year.



What is the maturity value for a $2,500
loan?



MV = P (1 + RT) Substitute known values.



MV = $2,500 ( 1 + 0.09 x 2)
(See next slide)
10

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


What is the maturity value?



MV = $2,500 ( 1 + 0.09 x 2)



MV = $2,500 (1 + 0.18)



MV = $2,500 (1.18)



MV = $2,950



Marcus will pay $2,950 at the end of
two years.

11
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Try these examples.


Terry Williams is going to borrow
$4,000 at 7.5% interest. What is the

maturity value of the loan after three
years?
 $4,900



Jim Sherman will invest $3,000 at 8%
for 5 years. What is the maturity value
of the investment?
 $4,200
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


11.1.3 Convert months to a
fractional or decimal part of a year.


Write the number of
numerator of a fraction.

months

as

the



Write 12 as the denominator of the fraction.



Reduce the fraction to lowest terms if using
the fractional equivalent.



Divide the numerator by the denominator to
get the decimal equivalent of the fraction.

13
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Convert the following to fractional
or decimal part of a year.


Convert 9 months and 15 months,
respectively, to years, expressing
both as fractions and decimals.



9/12 = ¾ = 0.75



9 months = ¾ or 0.75 of a year



15/12 = 1 3/12 = 1 ¼ = 1.25



15 months = 1 ¼ or 1.25 of a year.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Look at this example.


To save money, Stan Wright invested
$2,500 for 45 months at 3 ½ % simple
interest. How much interest did he
earn?



45 months = 45/12 = 3.75



I=PxRxT



I = $2,500 x 0.035 x 3.75



I = $328.13



Stan will earn $328.13
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Try these examples.


Akiko is saving a little extra money to
pay for her car insurance next year. If
she invests $1,000 for 18 months at
4%, how much interest can she earn?
 $60



Habib is going to borrow $2,000 for
42 months at 7% . What will the
amount of interest owed be?

 $490
16

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


11.1.4 Find the principal, rate or time
using the simple interest formula.

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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Find the principal using the simple
interest formula.


P = I / RT



Judy paid $108 in interest on a loan that
she had for 6 months. The interest rate
was 12%. How much was the principal?



Substitute the known values and solve.



P = 108/ 0.12 x 0.5



P = $1,800
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Find the rate using the simple
interest formula.


R = I / PT



Sam wants to borrow $1,500 for 15
months and will have to pay $225 in
interest. What is the rate he is being
charged?



Substitute the known values and solve.



R = 225/ $1,500 x 1.25



R = .12 or 12%



The rate Sam will pay is 12%.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Find the time using the simple
interest formula.


T = I / RP



Shelby borrowed $10,000 at 8% and
paid $1,600 in interest. What was the
length of the loan?



Substitute the known values and solve.



T = $1,600/0.08 x $10,000



T=2



The length of the loan was two years.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


11.2 Ordinary and Exact
Time and Interest


Find ordinary and exact time.



Find the due date.



Find the interest using the ordinary
and exact interest rates.



Find simple interest using a table.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


11.2.1 Find ordinary and
exact time.


Ordinary time: time that is based on
counting 30 days in each month.



Exact time: time that is based on counting
the exact number of days in a time period.

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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Examples


The ordinary time from July 12 to
September 12 is 60 days.



To find the exact time from July 12 to
September 12, add the following:
Days in July
Days in August

(31 -12 =)

19

31

Days in September

+12

62 days
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Sequential Numbers for
Dates of the Year


Find the exact time of a loan using the
sequential numbers table.
(Table 11-1 in the text)



If the beginning and due dates of the
loan fall within the same year, subtract
the beginning date’s sequential number
from the due date’s sequential number.



Ex.: From May 15 to October 15



288-135 = 153 days is the exact time.
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Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved


Beginning and due dates in
different years.


Subtract the beginning date’s
sequential number from 365.



Add the due date’s sequential number

to the result from the previous step.



If February 29 falls between the two
dates, add 1. (Is it a leap year?)
25

Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved