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Chapter 10
Simple Interest
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McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
#10
Simple Interest
Learning Unit Objectives
LU10.1 Calculation of Simple Interest and Maturity
Value
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•
Calculate simple interest and maturity value for
months and years
•
Calculate simple interest and maturity value by
(a) exact interest and (b) ordinary interest
Maturity Value
Maturity Value (MV) = Principal (P) + Interest (I)
The amount of the loan
(Face value)
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Cost of
borrowing
money
Simple Interest Formula
Simple Interest (I) = Principal (P) x Rate (R) x Time (T)
Beg. amount
borrowed
Stated as a
Percent
Stated in
years
Ryan borrowed $20,000. The loan was for 6 months at
a rate of 9%. What is interest and maturity value?
SI = $20,000 x.09 x 6 = $900 MV = $20,000 + $900 = $20,900
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Calculate Simple Interest
• LoanStar bank is offering a $10,000 year loan with
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7.5% interest. How much will the interest be at the end
of the year?
I=PXRXT
I = 10,000 x .075 x 1 = $750
What is the Maturity value at the end of the year?
MV = P + I
MV = 10,000 = 750 = 10,750
Calculate Simple Interest
• LoanStar bank is offering a $4,000 monthly loan with
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8% interest. How much will the interest be at the end
of the 4 months?
I=PXRXT
I = 4,000 x .08 x 4/12 = $106.67
What is the Maturity value at the end of the year?
MV = P + I
MV = 4,000 + 106.67 = 4106.67
How much interest will there be after two years?
I = 4,000 x .08 x 2 = 640
Two Methods of Calculating Simple Interest
and Maturity Value
Exact Interest (365 Days)
Ordinary Interest (360 Days)
Bankers Rule
Time = Exact number of days
365
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Time = Exact number of days
360
Simple Interest—Exact
• Using Exact Interest:
• I = P x R x T (days/365)
• A loan is taken for $20,000, payable in 90 days at a rate
of 9%. What is the interest and maturity value?
• I = 20,000 x .09 x 90/365
• I = 443.84
• MV = 20,443.84
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Simple Interest--Ordinary
• Using Ordinary Interest:
• I = P x R x T (days/360)
• A loan is taken for $25,000, payable in 90 days at a rate
of 9%. What is the interest and maturity value?
• I = 25,000 x .09 x 90/360
• I = 562.5
• MV = 25,562.50
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Calculate using Exact Interest
• John goes to WeTrustEm Bank to get a loan to buy a
car. He needs to borrow $7,500. He will be receiving
his tax refund in 60 days, so the bank offers him a loan
for 6% for the 60 days. The bank uses exact interest.
• What is the total amount John must pay back to the
bank after 60 days?
• 7500 x .06x 60/365 = 73.97 + 7500 = 7573.97
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Calculate using Ordinary Interest
• John decided he cannot afford the $7500 loan. He
found a different car for $5450. He goes to
MoneyLenders to get a loan, and agrees to a 90 day
period at 6.5%, with ordinary interest calculated.
• What must John repay for this loan?
• 5450 * .065 * 90/360 = 88.56 + 5450 = 5538.56
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Finding Days in a Loan Period
• Calendar Method—Exact days (365 days)
• Count the days between the beginning of the loan, and the
payment date
• Don’t count the initial day of the period
• Table method—Exact days
• Find the number of the beginning day
• Add the number of days in the period to this
• Find this numbered day as your due date
• Ordinary Interest—360 days
• Assume each month has 30 days
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Finding Days in a Loan Period
• A note made on Sept. 15 was repaid on Nov. 30; use
the calendar method. How many days?
• Sept 15 to Sept 30 = 30 – 15 = 15
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• Total =
Oct. 1 to Oct 31 = 31
Nov 1 to Nov 30 = 30
76 days
• A note made on Sept 20 was repaid on March 15; use
the table
• Sept 20 = 263; Dec 31 = 365; 365 – 263 = 102
• To March 15—day 74; 102 + 74 = 176
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Finding the Due Date of a Loan
• A 60-day note was signed on Sept. 20. When is the due
date of the loan, using the calendar method.
• Sept 20—30 = 10
• Oct
•
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31
Nov
41 days
19
60
Finding the Due Date of a Loan
• A 60-day note was signed on Sept. 20. When is the due
date of the loan, using the table method.
• Sept 20 = day
263
• Add days
+60
• Due day number 323
• Nov. 19
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Finding the Due Date of a Loan
• A note due in 120 days was made on Oct. 18. Use the
table method to find the date the note is due.
• Oct 18 = 291
• Dec 31 = 365
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days
74
• 120 – 74 = 46 days remaining
• 46 = Feb 15
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Assignment
• Review pps. 243—246
• Work Drill problems #10-1 to 10-9, p. 253
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Chapter 10
Simple Interest
1-19
McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
Review—finding due date
• A 120 day note was made on June 23. What is the due
date of this note?
• June 23 = 174
• + 120
•
294 = Oct. 21
• A 90 day note is due on Feb. 27. On what date was this
note made?
• Feb 27 = 58
• -90
• 32 back in previous year
• 365 – 32 = 333 = Nov. 29
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Review—finding Maturity of a Note
• Sara borrowed $2500 today from Good Deal Credit
Union. She promised to pay it back in full by the end
of the year, with 8% interest. How much must Sara
pay on Dec. 31 ?
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#10
Simple Interest
Learning Unit Objectives
LU10.2 Finding Unknowns in Simple Interest
Formula
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Using the interest formula, calculate the
unknown when the other two (principal, rate, or
time) are given
Using the Formula--Interest
I=PxRxT
We will assume Ordinary Interest
I
PxRxT
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Using the Formula--Principle
P = I / (R * T)
I
PxRxT
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Using the Formula--Rate
R = I / (P * T)
I
PxRxT
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Using the Formula--Time
T = I / (P * R)
I
PxRxT
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Finding Unknown in Simple Interest
Formula - Principal
Interest (I) = Principal (P) x Rate (R) x Time (T)
Principal = Interest
Rate x Time
$44
.
P = .11 x (120/360)
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Christina Jones paid
the bank $44 interest
at 11% for 120 days.
How much did she
borrow?
Finding Unknown in Simple Interest
Formula - Principal
Interest (I) = Principal (P) x Rate (R) x Time (T)
Principal = Interest
Rate x Time
.11 times 120
divided by
360. Do not
round answer
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$44
.
P = .036666667
Christina Jones paid
the bank $44 interest
at 11% for 120 days.
How much did she
borrow?
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Finding Unknown in Simple Interest
Formula - Principal
Interest (I) = Principal (P) x Rate (R) x Time (T)
Principal = Interest
Rate x Time
.11 times 120
divided by
360. Do not
round answer
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Christina Jones paid
the bank $44 interest
at 11% for 120 days.
How much did she
borrow?
$44
.
P = .11 x (120/360) = $1,200
Finding Unknown in Simple Interest
Formula - Rate
Interest (I) = Principal (P) x Rate (R) x Time (T)
Rate =
Interest
Principal x Time
Christina Jones
borrowed $1,200 from
the bank. Her interest
is $44 for 120 days.
What rate of interest
did Christina pay?
$44
.
R = $1,200 x (120/360) =
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Finding Unknown in Simple Interest
Formula - Rate
Interest (I) = Principal (P) x Rate (R) x Time (T)
Rate =
Interest
Principal x Time
$44 .
R = 400 = .11
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Christina Jones
borrowed $1,200 from
the bank. Her interest
is $44 for 120 days.
What rate of interest
did Christina pay?
Finding Unknown in Simple Interest
Formula - Time
Interest (I) = Principal (P) x Rate (R) x Time (T)
Time =
Interest
Principle x Rate
$44
.
T = $1,200 x .11
T =
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$44
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.
Christina Jones
borrowed $1,200 from
the bank. Her interest
is $44 for 11%. How
much time does
Christina have to
repay the loan?
Finding Unknown in Simple Interest
Formula - Time
Interest (I) = Principal (P) x Rate (R) x Time (T)
Time =
Interest
Principle x Rate
$44
.
T = $1,200 x .11 = .33
Christina Jones
borrowed $1,200 from
the bank. Her interest
is $44 for 11%. How
much time does
Christina have to
repay the loan?
Convert years to days (assume 360
days)
.33 x 360 = 120 days
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Use the Interest Formula
• A loan for $157,000 was charged 10.75% interest. The
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interest amounted to $6,797.88. What amount of time
was this loan for?
T = I/P*R
T =6797.88 / (.1075* 157000)
T = 6797.88 / 16877.5
T = .40278
T= .40278 * 360 = 145 days
Use the Interest Formula
• A loan for $7,500 charged interest of $350. The loan
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was paid in 120 days. What interest rate was charged?
R=I/P*T
R = 350 / (7500*120/360)
R = 350 / 2500
R = .14 = 14%
Use the Interest Formula
• A loan for 120 days with 9% interest shows a total
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interest due of $103. What was the original amount of
the loan?
P=I/R*T
P = 103 / (.09 * 120/360)
P = 103 / .03
P = $3433.33
Assignment
• review pps. 246—248
• work drill problems 10-10 to 10-12, p. 254
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Chapter 10
Simple Interest
1-38
McGraw-Hill/Irwin
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
Interest Formula—review 1
• A loan for $55,000 charged interest of
$1,100. The loan was paid in 90 days.
What interest rate was charged?
• R=I/P*T
• R = 1100 / (55000*90/360)
• R = .08 = 8%
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Interest Formula—review 2
• A loan for $50,000 was charged 7.75% interest. The
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interest amounted to $1453.13. What amount of time
was this loan for?
T = I/P*R
T =1453.13 / (.0775* 50000)
T = 1453.13 / 3875
T = .375
T= .375 * 360 = 135 days
Interest Formula—review 3
• A loan for 2 years with 9% interest shows a total
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interest due of $459. What was the original amount of
the loan?
P=I/R*T
P = 459 / (.09 * 2)
P = 459 / .18
P = $2550
Interest Formula—review 4
• A loan for $45,000 at 6.5% was made on Nov. 15. The
loan was repaid on March 31. What was the amount of
interest on the loan using exact interest? What was the
maturity value?
• I=PxRxT
• I = 45000 x .065 x 136/365
• I = 1089.86
• MV = 46089.86
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#10
Simple Interest
Learning Unit Objectives
LU10.3 U.S. Rule -- Making Partial Note Payments
before Due Date
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•
List the steps to complete the U.S. Rule
•
Complete the proper interest credits under the
U.S. Rule
U.S. Rule - Making Partial Note Payments
before Due Date
Any partial loan payment first covers any
interest that has built up. The remainder of
the partial payment reduces the loan
principal.
Allows the borrower to receive proper interest credits
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Using the U.S. Rule
Step 1. Calculate interest on principal from date of loan
to date of first principal payment
Step 2. Apply partial payment to interest due. Subtract
remainder of payment from principal
Step 3. At maturity, calculate interest from last partial
payment. Add this interest to adjusted balance.
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U.S. Rule - Example
Darren owes $3,000 on an 10%, 90 day note. On day 40, Darren pays $1,200
on the note. Assume a 360- day year. What is Darren’s Adjusted balance
after day 40? What is the ending balance due?
Step 1. Calculate interest on principal
from date of loan to date of first principal
payment
Step 2. Apply partial payment to interest
due. Subtract remainder of payment from
principal
Step 3. At maturity, calculate interest
from last partial payment. Add this
interest to adjusted balance.
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$3,000 x .10 x 40 = $33.33
360
$1,200 - 33.33 = $1,166.67
$3,000 - 1,166.67 = $1,833.33
$1,833.33 x .10 x 50 = $25.46
360
$25.46 + $1,833.33 = $1,858.79
Use the U.S. Rule
• Jesse borrowed $10,800 on a 1-
year note at 14%. After 60
days, Jesse received a tax
refund and paid $2,500 on the
note. On her birthday, day 200
of the loan, Jesse received a
$5,000 check from her
Grandmother, and she applied
it toward her loan. What will
be the total interest and final
balance due on the loan?
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•
Jesse borrowed $10,800 on a 1-year note at 14%. After 60 days, Jesse received a tax
refund and paid $2,500 on the note. On her birthday, day 200 of the loan, Jesse
received a $5,000 check from her Grandmother, and she applied it toward her loan.
What will be the total interest and final balance due on the loan?
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Step 1. 10,800 x .14 x 60/360 = 252
Step 2. 2500 – 252 = 2248 (applied against principle)
10,800 – 2248 = 8552 (new principle balance)
Find number of days in second period
200 – 60 = 140
repeat step 1 & 2 for second payment
8552 x .14 x 140/360 = 465.61
5000 – 465.61 = 4534.39 (applied against principle)
8552 – 4534.39 = 4017.61 (new principle balance)
Step 3. find days remaining: 360 – 200 = 160
4017.61 x .14 x 160/360 = 249.98
Final balance due: 4017.61 + 249.98 = 4,267.59
Total interest cost: 252.00 + 465.61 + 249.98 = 967.59
#10-13
• 10000 x .08 x 100/360 = 222.22 interest
• 4000 – 222.22 = 3777.78 apply to principal
• 10000 – 3777.78 = 6222.22 adjusted balance
• 6222.22 x .08 x 80/360 = 110.62 interest
• 2000 – 110.62 = 1889.38 to principal
• 6222.22 – 1889.38 = 4332.84 new balance
• 4332.84 x .08 x 60/360 = 57.77 interest
• 4332.84 + 57.77 = 4390.61 balance due
• 222.22 + 110.60 + 57.77 = 390.61 total interest
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Assignment
• Review pps. 249—251
• work Drill problem 10-13, p. 254
• do Word Problems #14--23
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