49 Business Math _ 123

 Find the principal, rate or time using the simple interest formula...  Rate : the percent of the principal paid as interest per time period.. 11.1.4 Find the principal, rate or time u

Business Math

Chapter 11:

Simple Interest and

Simple Discount

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.

Key Terms

use of money.

loan or investment is repaid in a lump sum.

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.

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 = P x R x T

Find the simple interest using the simple interest formula

Identify the principal,

rate and time

P= R x B

 The interest is a percentage

 Principal is the amount borrowed or

invested.

time period, usually one year.

unit of time as the rate (i.e one year)

Find the interest paid on a loan.

Try these examples.

 Find the interest on a 2-year loan of

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)

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)

What is the maturity value?

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

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

 Write the number of months as the numerator of a fraction.

 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.

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.

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

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

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

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

 R = I / PT

months and will have to pay $225 in

interest What is the rate he is being charged?

 R = 225/ $1,500 x 1.25

 R = 12 or 12%

Find the rate 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

Find the time using the simple

interest formula.

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.

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.

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.

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?)

Look at this example.

 Find the exact time from May 15 on

Year 1 to March 15 in Year 2.

 365 – 135 = 230

 230 + 74 = 304 days

 The exact time is 304 days

 Note: If Year 2 is a leap year, the

exact time is 305 days.

Try this example.

 A loan made on September 5 is due

July 5 of the following year

 Find: a) ordinary time

b) exact time in a non-leap year c) exact time in a leap year.

 Ordinary time = 300 days

 Exact time (non-leap year) = 303 days

 Exact time (leap year) = 304 days

11.2.3 Find the ordinary interest rate per day

and the exact interest rate per day.

 Ordinary interest : a rate per day that assumes 360 days per year.

 Exact interest : a rate per day that assumes 365 days per year.

 Banker’s rule : calculating interest on a loan based on ordinary interest and exact time which yields a slightly higher amount of interest.

Find the ordinary interest per day.

 For ordinary interest rate per day,

divide the annual interest rate by

360.

Ordinary interest rate per day =

Interest rate per year

360

Find the exact interest per day.

 For exact interest rate per day, divide the annual interest rate by 365.

Exact interest rate per day =

Interest rate per year

365

Use ordinary time to find the ordinary interest on a loan.

 A loan of $500 at 7% annual interest

rate The loan was made on March 15 and due on May 15 (Principal = $500) I

= P x R x T

 Length of loan ( ordinary time ) = 60 days

 Rate = 0.07/360 (ordinary interest)

 Interest = $500 x 0.07/360 x 60

Find the ordinary interest using

exact time for the previous loan.

 A loan of $500 at 7% annual interest

rate The loan was made on March 15 and due on May 15 (Principal = $500) I

= P x R x T

 Length of loan ( exact time ) = 61 days

 Rate = 0.07/360 (ordinary interest)

 Interest = $500 x 0.07/360 x 61

Find the exact interest using exact

time for the previous loan.

 A loan of $500 at 7% annual interest

rate The loan was made on March 15

and due on May 15 (Principal = $500) I

= P x R x T

 Length of loan ( exact time ) = 61 days

 Rate = 0.07/365 (exact interest)

 Interest = $500 x 0.07/365 x 61

11.2.4 Find simple interest

using a table.

1 Identify the amount of money that the

table uses as the principal (Usually $1,

$100 or $1000)

2 Divide the loan principal by the table

principal.

3 Select the days row corresponding to

the time period (in days) of the loan.

(continue on next slide)

Find simple interest

using a table.

4 Select the annual rate column

corresponding to the annual interest rate of the loan.

5 Locate the value in the cell where the two intersect.

6 Multiply the quotient from step 2 by the value from step 5.

Look at this example.

 Find the exact interest on a loan of

$6,500 at 7.5% annually for 45 days.

 Use Table 11-2 in your text to locate the interest for $100 Move across

the 45-days row to the 7.5% column

Try these examples.

 Find the exact interest on a $5,000

loan for 30 days at 8%.

 $32.88

 Find the exact interest on a $1,800

loan for 20 days at 8.5%.

 $8.38

11.3.1 Find the bank discount and proceeds

for a simple discount note.

 For the bank discount , use:

Bank discount = face value x disc rate

x time

[I = P x R x T]

 For the proceeds , use:

Proceeds = face value – bank discount

A = P - I

A promissory note

11.3.2 Find the third party discount and proceeds for a third party discount note.

 For the bank discount, use:

the original note x discount rate x

discount period.

 For the proceeds, use:

note – third-party discount

A = P - I

Look at this example.

 Mihoc Trailer Sales made a note of

August 12 and due November 10 Since

Mihoc Trailer Sales needs cash, the note is taken to a third party on September 5

with a 13% annual discount using the

banker’s rule.

 Find the proceeds of the note.

Mihoc Trailer Sales

 To find the proceeds, we find the

maturity value of the original note ,

then the third-party discount

 Exact time is 90 days (314-224)

 Exact interest rate is 09/365

 MV = P(1+ RT)

 MV = $10,000 ( 1 + 0.09/365 x 90)

 MV = $10.221.92

Find the proceeds of the note.

 Exact time of the discount period is 66 days (314 - 248) period between Sept 5 and Nov 10.

 Ordinary discount rate is 0.13/ 360.

 Third party discount = I = PRT

 Third party discount = $10,221.92 ( 0.13/360) (66)

 Third party discount = $243.62

 Proceeds = A = P – I

 Proceeds = $10,221.92 - $243.62 = $9,978.30