# Simple Interest Formula - Excel by ofm18586

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```									                  Chapter 08: Simple Interest
What is Interest?
Solve for simple interest
I = P*R*T
Calculate maturity value
Determine the number of days from one date to another
Exact Simple Interest
Ordinary Simple Interest
What is a Note?
Due date of Note
Find Principal
P = I/(R*T)
Find Rate
R = I/(P*T)
Find Time
T = I/(P*R)
Discount Notes
Bank Discount
Proceeds
Face Value
Effective Interest Rate for Simple Interest Discount Note
Interest:
Interest is rent paid on money
Firms, businesses and individuals borrow money in order to
invest the money and earn a higher rate of return than the
interest rate
Firms, businesses and individuals invest money to earn
interest

Principal:
Amount borrowed, lent out, or invested

Simple Interest:
Interest paid on only the principal

Compound Interest:
Interest paid on principal and past interest also known as
"interest on interest"

Simple Interest Rate:
Annual % rate paid or received
Calculate Simple Interest
I = Simple interest
P = Principal
R = Interest Rate
T = Time in YEARS               ** If you are given time in months or days, you must convert it to years

I=P*R*T
Hank’s Auto shop takes out a loan from the bank for \$10,000 in order to buy new equipment. Hank is considering whether he
should take out the loan for 6 months at 7% or 1.5 years at 10%. Find the simple interest on both loans.

Step 1: List details:

Loan # 1
Principal =                      \$                  10,000.00
Rate =                                                  7.00%
Time =                                                       6 Months

Loan # 2
Principal =                      \$                  10,000.00
Rate =                                                 10.00%
Time =                                                      1.5 Years

Step 2: Set up and solve

Loan # 1                                                         Loan # 2

Convert Time to years = 6
Months/12 Months = 6/12 =

I = P*R*T =                                                     I = P*R*T = \$10,000.00*0.1*1.5
\$10,000.00*0.07*6/12 =                                          =

Step 3: State in words
erest

t convert it to years

equipment. Hank is considering whether he
he simple interest on both loans.

Loan # 2

<== Do not have to
round because we are
not using these
numbers in any
subsequent
calculations. The
formatted display of
the number is
sufficient.
Calculate Maturity Value
P = Principal
I = Simple interest
P + I = Maturity Value

M=P+I
Christina takes out a \$6,500.00 loan for 30 months at 10% interest in order to buy a used Jetta. Find the
interest due on the loan and the maturity value.

Principal =                                \$           6,500.00
Time =                                                        30 Months
Simple Interest Rate =                                   10.00%

Interest = 6500*0.1*30/12 =                                       =ROUND(B11*B13*B12/12,2) (because we are going to add
Principal =
P + I = Maturity Value = 6500 + 1625 =
because we are going to add it to principal later)
Find The Number Of Days From One Date To Another
Find the number of days from November 4 to February 21

1)               To do it by hand you have to look at a calendar or use the knuckle trick or learn the Rhyme method
Sunday, November 04, 2007 Saturday, December 01, 2007 Tuesday, January 01, 2008
Friday, November 30, 2007    Monday, December 31, 2007 Thursday, January 31, 2008
26                             31                            31

Total Days =                                                     109

To do it in Excel you put the two date in two different cells, and then in a third cell subtract the earlier date from th
2)                  date (this method fits the requirement of not counting the start date and counting the end date)
Earlier date                            Sunday, November 04, 2007
Later date                              Thursday, February 21, 2008
Total days from 11/4/07 to 2/21/08                                                        Remember the keyboard
shortcut for "General Number
Format" ==> Ctrl + Shirt + ~
Earlier date                                Friday, February 23, 2007
Later date                                  Saturday, March 24, 2007
Total days from 2/23/07 to 3/24/07
Date To Another
ary 21

k or learn the Rhyme method
Friday, February 01, 2008
Thursday, February 21, 2008
21

ll subtract the earlier date from the later
and counting the end date)

Remember the keyboard
shortcut for "General Number
Format" ==> Ctrl + Shirt + ~
I=P*R*T
Number of days assumed in one year = 365
Exact Interest time =                   # of days in the loan period/365

Number of days assumed in one year = 360
Ordinary Interest time =                 # of days in the loan period/360

Find the exact interest and the banker’s interest given the following data:
Principal = \$10,000                                   \$                     10,000.00
Simple interest = 10%                                                           10.00%
Loan taken out on                                                      January 1, 2007
Loan paid back on                                                         July 31, 2007

Exact Interest time                                                                  Ordinary In
Total days from 1/1/07 to 7/31/07 =
Number of days assumed in one year =

Interest = P * R * T = \$10,000 * 0.1 * 211/ =
=P*R*T
assumed in one year = 365
This will always be smaller because you are comparing the same thing to a
bigger number (think of 1/3 compared to 1/2)

assumed in one year = 360
This will always be bigger because you are comparing the same thing to a
smaller number (think of 1/2 compared to 1/3)

d the banker’s interest given the following data:

Ordinary Interest time
Total days from 1/1/07 to 7/31/07 =
Number of days assumed in one year =

Interest = P * R * T = \$10,000 * 0.1 * 211/ =
Notes
Promissory Notes:
A legal document in which on person or firm agrees to pay:
A stated amount of money
Plus interest computed at a stated rate
At a stated time in the future
To another person or firm
A promissory note is the written record of a loan

Maker or Payer or Debtor of the note:
The person borrowing the money

Payee or Creditor of the note:
The person lending the money

Term:
Length of time until the note is due

Face Value or Principal:
The principal amount due – the amount written of the face of the promissory note.

Simple Interest Note:
A promissory note for a loan in which the interest is calculated using the simple interest formula:
I = PRT = Face Value x Simple Interest Rate x Time
erest formula:
Find The Due Date Of A Note
When the term for a loan is given in DAYS, count the number of days from the day after the promissory
date.

Example:
When is a 90-day loan made on January 15, 2004 due?
Date
Term length
Due Date

When the term for a loan is given in MONTHS, the loan is due on the same day the loan is made, after t
of months has passed
If the date should be at the end of the month, but that day does not exist, use the last day of the month, a
as the due date
When the loan term is given in months, do not convert the time to days in order to find the due da

Example:
When is a 6-month loan made on January 15, 2004 due?
It is due on the 15th, 6 months later:
Term of loan
Note Issue Date
Due Date

Example:
When is a 3-month note made on January 31 due?
It is due on April 31, but April 31 does not exist.
The due date becomes April 30.
Term of loan
Note Issue Date
Due Date
e Date Of A Note
number of days from the day after the promissory note issue
date.

xample:
1/15/2004
90
days

n is due on the same day the loan is made, after the number
hs has passed
day does not exist, use the last day of the month, as it exists,

different
he due date
convert the time to days in order to find the due date.

xample:

6 Months
Thursday, January 15, 2004
=EDATE(B12,B10) months

xample:

3 Months
Saturday, January 31, 2004
=EDATE(B19,B18)
Example 1: If you take out a 90 days, \$5,000.00 loan with a simple interest rate of 7.25% on January 6, 2004, what is the due
and maturity value (use 365 days in a year)?

Step 1: List Details:
Term                                                                             90 days
Principal                                           \$                     5,000.00
Simple Interest Rate =                                                       7.25%
Note Issue Date                                           Tuesday, January 06, 2004
Days in the Year                                                                365

Step 2: Set up and solve
Interest = P * R * T = \$5,000 * 0.0725 * 90/365 =                                     =ROUND(B5*B6*B4/B8,2) (must round b
Principal =                                                                           =B5
Maturity Value                                                                        =SUM(B12:B13)
Due Date                                                                              =B7+B4

Step 3: State in Words

Example 2: If you take out a 6 month, \$3,800.00 loan with a simple interest rate of 11.00% on March 2, 2004, what is the due
and maturity value?

Step 1: List Details:
Term                                                                              6 months
Principal                                           \$                     3,800.00
Simple Interest Rate =                                                      11.00%
Note Issue Date                                             Tuesday, March 02, 2004
Months in the Year                                                               12

Step 2: Set up and solve
Interest = P * R * T = \$3,800 * 0.11 * 6/12 =                                         =ROUND(B25*B26*B24/B28,2)
Principal =                                                                           =B25
Maturity Value                                                                        =SUM(B32:B33)
Due Date                                                                              =EDATE(B27,B24)

Step 3: State in Words
nuary 6, 2004, what is the due date

B5*B6*B4/B8,2) (must round because we are going to use it in a later calculation)

March 2, 2004, what is the due date

B25*B26*B24/B28,2)
Find Principal Given Interest, Rate, & Time

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia borrows a principal amount that earns \$50.00 interest for the lender, the simple interest rate on the loan is 10.00%, a
is out for 180 days. Find the principal amount.

Step 1: List Details:
Interest                                    \$        50.00
Principal
Rate                                                10.00%
Time                                                    180 days
Days in a year                                          365

Step 2: Set up and solve
<== Do not have to rou
Principal = I/(R*T) = 50/(0.1*180/365) =                      =B12/(B14*B15/B16)                       because we are not usin
any subsequent calcula
formatted display of the
sufficient.
Check with Interest = P*R*T ==>                               =B21*B14*B15/B16

Step 3: State in Words
Time

interest rate on the loan is 10.00%, and the loan
nt.

<== Do not have to round
because we are not using this in
any subsequent calculations. The
formatted display of the number is
sufficient.
Find Rate Given Interest, Principal, & Time

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia borrows \$750.00 and pays \$75.00 interest. If the loan is out for 270 days, find the interest rate.

Step 1: List Details:
Interest                                         \$         75.00
Principal                                        \$        750.00
Rate
Time                                                          270 days
Days in a year                                                365

Step 2: Set up and solve

Rate = I/(P*T) = \$75.00/(\$750.00*270/365) =                        =B12/(B13*B15/B16)

Check with Interest = P*R*T ==>                                    =B12/(B13*B15/B16)

Step 3: State in Words
me

0 days, find the interest rate.

<== Do not have to round
because we are not using this in
any subsequent calculations.
The formatted display of the
number is sufficient.
Find Time Given Interest, Principal, & Rate

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia deposits \$10,000.00 in a savings account at an interest rate of 10.00%. If she earns \$750.00 interest, how many da
the account?

Step 1: List Details:
Interest                                                     \$        750.00
Principal                                                    \$     10,000.00
Rate                                                                  10.00%
Time                                                                            days
Days in a year                                                            360

Step 2: Set up and solve

Time (in years) = I/(P*R) = \$750.00/(\$10,000.00*10.00% =                        =B12/(B13*B14)
Time in days = *360 =                                                           =B21*B16

Check with Interest = P*R*T ==>                                                 =B13*B14*B22/B16

Step 3: State in Words

Find Time Given Interest, Principal, & Rate

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time I/(P*R)

Gardenia deposits \$10,000.00 in a savings account at an interest rate of 10.00%. If she earns \$750.00 interest, how many mon
the account?

Step 1: List Details:
Interest                                                     \$        750.00
Principal                                                    \$     10,000.00
Rate                                                                  10.00%
Time                                                                            months
Months in a year                                                            12
Step 2: Set up and solve

Time I/(P*R) = \$750.00/(\$10,000.00*10.00% =                          0.750 =B12/(B13*B14)
Time in days = 0.75*12 =                                                 9 =B21*B16

Step 3: State in Words

From the data presented, we calculated the Time to be 9 months.
cipal, & Rate

)

arns \$750.00 interest, how many days did she leave the money in

<== Do not have to round because we
want to use the unrounded decimal to
multiply times the number of days in a
e                       year. (We need the unrounded decimal
so that we get the actual number of
days).

cipal, & Rate

rns \$750.00 interest, how many months did she leave the money in
e

Time to be 9 months.
Simple Discount Notes or “Interest in Advance Notes”:

The idea of a Simple Discount Note is:
1                 You go to the bank and ask to borrow \$1,000
The bank says sure, but we will only give you \$900 today, then you have to
2                     pay use the \$1,000 back in one year
3       You say: "What??!? Why only \$900, if I have to pay back \$1,000?"
The bank says: "We are going to collect the \$100 interest up front. This is
4                        called a Simple Discount Note."

Simple Discount Notes or “Interest in Advance Notes”:
The bank collects the interest in advance
The borrower pays the full face value back on the due date
The borrower receives the face value minus the interest on the day that the funds
are disbursed.
The amount the borrower receives is called “Proceeds”
The interest in advance is called “bank discount” or “discount”
Example: Principal (face value)        - Interest (Discount)       = Proceeds

\$              1,000.00 - \$                  100.00 = \$ 900.00

The trick the bank is playing is that it will tell you that the rate is 10%, but
really the Effective Simple Interest Rate = \$100.00/\$900.00 = 11.11% or
11 1/9%
Simple Interest                               >> Face Value or Principal            +
Simple Discount                               >> Proceeds                           +
** The face value and the maturity value are the same for a S. discount note

Bank Discount                                  = Face Value or Maturity Value         *
B                                              = M                                    *

Proceeds                                       = Face Value or Maturity Value         -
P                                              = M                                    -

Example 1:
If you take out a loan with a maturity value (face value) of \$2000 and the bank discount is \$150, what are the
proceeds?

Step 1: List Details:
Face Value or Maturity Value                   =     \$                     2,000.00
Bank Discount                                  =     \$                       150.00

Step 2: Set up and solve

Proceeds                                       = Face Value or Maturity Value         -
P                                              = M                                    -
=                                      -

Step 3: State in Words

Example 2:
Cynthia Thomas signs an \$8500, 9-month note. If the bank discounts the note at 9%, find the amount of the discount
and proceeds.

Step 1: List Details:
Face Value or Maturity Value                   =                           8,500.00
Time                                           =                                   9 months
Discount Rate (Interest Rate)                  =                              9.00%
Months in the year                             =                                  12

Step 2: Set up and solve

Bank Discount                                  = Face Value or Maturity Value         *
B                                              = M                                    *

Bank Discount = \$8,500.00*09.00%*9/12 =        =

Proceeds = 8500-573.75 =                       =

Step 3: State in Words
.
Interest                           Repayment amount
Interest                         = Maturity Value
Bank Discount                    = Face Value or Maturity Value
value are the same for a S. discount note

Discount Rate (Interest Rate)    * Time
D                                * T

Bank Discount
B

the bank discount is \$150, what are the

Bank Discount
B

note at 9%, find the amount of the discount

months

Discount Rate (Interest Rate)    * Time
D                                * T

=ROUND(C33*C35*C34/C36,2)
If you know the proceeds you want, how do you figure out the amount to
borrow, the maturity value or face value?

Formula = Maturity Value = Proceeds / (1 - Discount Rate * Time) =
M = P/(1-D*T) =

Example 1:
Mike Modigliani needs \$4000 to buy a machine. Find the amount he needs to
borrow (maturity value) if he plans to repay the note in 180 days and the bank
charges a 12% discount rate.
<== Do not have to
Step 1: List Details:                     round because we
are not using this in
Proceeds                                              = \$       4,000.00
any subsequent
Discount Rate (interest Rate)                         =           12.00%
calculations. The
Time                                                  =               180 Days    formatted display of
Days in Year                                          =               360         the number is
sufficient.
Step 2: Set up and solve

M = P/(1-D*T) = \$4,000.00/(1-0.12*180/360)            =                     =C9/(1-C10*C11/C12)

Step 3: State in Words
<== Do not have to
round because we
are not using this in
any subsequent
calculations. The
formatted display of
the number is
sufficient.

=C9/(1-C10*C11/C12)

4255.3191
Simple Interest Note Simple Discount Note
Face Value                                                        7500                 7500
Interest                                                           225                  225
Amount available to borrower                                      7500                 7275
Maturity value                                                    7725                 7500
Time in days                                                        90                   90
Days in year                                                       360                  360

Effective Interest Rate Simple Interest Note =             0.1200000 =B3/(B2*B6/B7)

Effective Interest Rate Simple Discount Note =            0.12371134 =C3/(C4*C6/C7)
Calculate Simple Interest
I = Simple interest
P = Principal
R = Interest Rate
T = Time in YEARS                ** If you are given time in months or days, you must convert it to years

I=P*R*T
Hank’s Auto shop takes out a loan from the bank for \$10,000 in order to buy new equipment. Hank is considering whether he
should take out the loan for 6 months at 7% or 1.5 years at 10%. Find the simple interest on both loans.

Step 1: List details:

Loan # 1
Principal =                      \$                    10,000.00
Rate =                                                    7.00%
Time =                                                         6 Months

Loan # 2
Principal =                      \$                    10,000.00
Rate =                                                   10.00%
Time =                                                        1.5 Years

Step 2: Set up and solve

Loan # 1                                                          Loan # 2

Convert Time to years = 6
Months/12 Months = 6/12 =                                     0.5

I = P*R*T =                                                     I = P*R*T = \$10,000.00*0.1*1.5
\$10,000.00*0.07*6/12 =           \$                       350.00 =

Step 3: State in words

The simple interest on loan # 1 is \$350.00 for 1/2 of a year. The simple interest for loan # 2 is \$1,500.00 for 1.5 years.
erest

t convert it to years

equipment. Hank is considering whether he
he simple interest on both loans.

Loan # 2

<== Do not have to
round because we are
not using these
\$                     1,500.00   numbers in any
subsequent
calculations. The
formatted display of
the number is
t for loan # 2 is \$1,500.00 for 1.5 years.
sufficient.
Calculate Maturity Value
P = Principal
I = Simple interest
P + I = Maturity Value

M=P+I
Christina takes out a \$6,500.00 loan for 30 months at 10% interest in order to by a used Jetta. Find the interest
due on the loan and the maturity value.

Principal =                                 \$           6,500.00
Time =                                                         30 Months
Simple Interest Rate =                                    10.00%

Interest = 6500*0.1*30/12 =                 \$           1,625.00   =ROUND(B11*B13*B12/12,2) (because we are going to add
Principal =                                 \$           6,500.00
P + I = Maturity Value = 6500 + 1625 =      \$           8,125.00
because we are going to add it to principal later)
Find The Number Of Days From One Date To Another
Find the number of days from November 4 to February 21

1)               To do it by hand you have to look at a calendar or use the knuckle trick or learn the Rhyme method
Sunday, November 04, 2007 Saturday, December 01, 2007 Tuesday, January 01, 2008
Friday, November 30, 2007    Monday, December 31, 2007 Thursday, January 31, 2008
26                             31                            31

Total Days =                                                     109

To do it in Excel you put the two date in two different cells, and then in a third cell subtract the earlier date from th
2)                  date (this method fits the requirement of not counting the start date and counting the end date)
Earlier date                            Sunday, November 04, 2007
Later date                              Thursday, February 21, 2008
Total days from 11/4/07 to 2/21/08                               109                      Remember the keyboard
shortcut for "General Number
Format" ==> Ctrl + Shirt + ~
Earlier date                                Friday, February 23, 2007
Later date                                  Saturday, March 24, 2007
Total days from 2/23/07 to 3/24/07                                 29
Date To Another
ary 21

k or learn the Rhyme method
Friday, February 01, 2008
Thursday, February 21, 2008
21

ll subtract the earlier date from the later
and counting the end date)

Remember the keyboard
shortcut for "General Number
Format" ==> Ctrl + Shirt + ~
I=P*R*T
Number of days assumed in one year = 365
Exact Interest time =                   # of days in the loan period/365

Number of days assumed in one year = 360
Ordinary Interest time =                  # of days in the loan period/360

Find the exact interest and the banker’s interest given the following data:
Principal = \$10,000                                  \$                     10,000.00
Simple interest = 10%                                                          10.00%
Loan taken out on                                                     January 1, 2007
Loan paid back on                                                        July 31, 2007

Exact Interest time                                                                 Ordinary In
Total days from 1/1/07 to 7/31/07 =                                                 211
Number of days assumed in one year =                                                365

Interest = P * R * T = \$10,000 * 0.1 * 211/365 =       \$                   578.082192
=P*R*T
assumed in one year = 365
This will always be smaller because you are comparing the same thing to a
bigger number (think of 1/3 compared to 1/2)

assumed in one year = 360
This will always be bigger because you are comparing the same thing to a
smaller number (think of 1/2 compared to 1/3)

d the banker’s interest given the following data:

Ordinary Interest time
Total days from 1/1/07 to 7/31/07 =                                       211
Number of days assumed in one year =                                      360

Interest = P * R * T = \$10,000 * 0.1 * 211/360 =      \$           586.111111

Is \$586.11 bigger than \$578.08?
TRUE
Find The Due Date Of A Note
When the term for a loan is given in DAYS, count the number of days from the day after the promissory
date.

Example:
When is a 90-day loan made on January 15, 2004 due?
Date
Term length
Due Date

When the term for a loan is given in MONTHS, the loan is due on the same day the loan is made, after t
of months has passed
If the date should be at the end of the month, but that day does not exist, use the last day of the month, a
as the due date
When the loan term is given in months, do not convert the time to days in order to find the due da

Example:
When is a 6-month loan made on January 15, 2004 due?
It is due on the 15th, 6 months later:
Term of loan
Note Issue Date
Due Date

Example:
When is a 3-month note made on January 31 due?
It is due on April 31, but April 31 does not exist.
The due date becomes April 30.
Term of loan
Note Issue Date
Due Date
e Date Of A Note
number of days from the day after the promissory note issue
date.

xample:
1/15/2004
90
4/14/2004                     days

n is due on the same day the loan is made, after the number
hs has passed
day does not exist, use the last day of the month, as it exists,

different
he due date
convert the time to days in order to find the due date.

xample:

6 Months
Thursday, January 15, 2004
Thursday, July 15, 2004 =EDATE(B12,B10) months

xample:

3 Months
Saturday, January 31, 2004
Friday, April 30, 2004 =EDATE(B19,B18)
Example 1: If you take out a 90 days, \$5,000.00 loan with a simple interest rate of 7.25% on January 6, 2004, what is the due
and maturity value (use 365 days in a year)?

Step 1: List Details:
Term                                                                              90 days
Principal                                            \$                     5,000.00
Simple Interest Rate =                                                        7.25%
Note Issue Date                                            Tuesday, January 06, 2004
Days in the Year                                                                 365

Step 2: Set up and solve
Interest = P * R * T = \$5,000 * 0.0725 * 90/365 =    \$                          89.38    =ROUND(B5*B6*B4/B8,2) (must round b
Principal =                                          \$                       5,000.00    =B5
Maturity Value                                       \$                       5,089.38    =SUM(B12:B13)
Due Date                                                        Monday, April 05, 2004   =B7+B4

Step 3: State in Words

The maturity value of the loan is \$5,089.38 and the due date is April 5, 2004.

Example 2: If you take out a 6 month, \$3,800.00 loan with a simple interest rate of 11.00% on March 2, 2004, what is the due
and maturity value?

Step 1: List Details:
Term                                                                               6 months
Principal                                            \$                     3,800.00
Simple Interest Rate =                                                       11.00%
Note Issue Date                                              Tuesday, March 02, 2004
Months in the Year                                                                12

Step 2: Set up and solve
Interest = P * R * T = \$3,800 * 0.11 * 6/12 =        \$                       209.00      =ROUND(B25*B26*B24/B28,2)
Principal =                                          \$                     3,800.00      =B25
Maturity Value                                       \$                     4,009.00      =SUM(B32:B33)
Due Date                                              Thursday, September 02, 2004       =EDATE(B27,B24)

Step 3: State in Words

The maturity value of the loan is \$4,009.00 and the due date is September 2, 2004.
nuary 6, 2004, what is the due date

B5*B6*B4/B8,2) (must round because we are going to use it in a later calculation)

5, 2004.

March 2, 2004, what is the due date

B25*B26*B24/B28,2)

ber 2, 2004.
Find Principal Given Interest, Rate, & Time

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia borrows a principal amount that earns \$50.00 interest for the lender, the simple interest rate on the loan is 10.00%, a
is out for 180 days. Find the principal amount.

Step 1: List Details:
Interest                                    \$        50.00
Principal
Rate                                                10.00%
Time                                                    180 days
Days in a year                                          365

Step 2: Set up and solve
<== Do not have to rou
Principal = I/(R*T) = 50/(0.1*180/365) =            1013.89 =B12/(B14*B15/B16)                         because we are not usin
any subsequent calcula
formatted display of the
sufficient.
Check with Interest = P*R*T ==>                          50 =B21*B14*B15/B16         Checks out!!

Step 3: State in Words

From the data presented, we calculated the Principal to be \$1,013.89.
Time

interest rate on the loan is 10.00%, and the loan
nt.

<== Do not have to round
because we are not using this in
any subsequent calculations. The
formatted display of the number is
sufficient.

be \$1,013.89.
Find Rate Given Interest, Principal, & Time

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia borrows \$750.00 and pays \$75.00 interest. If the loan is out for 270 days, find the interest rate.

Step 1: List Details:
Interest                                         \$         75.00
Principal                                        \$        750.00
Rate
Time                                                          270 days
Days in a year                                                365

Step 2: Set up and solve

Rate = I/(P*T) = \$75.00/(\$750.00*270/365) =               13.52% =B12/(B13*B15/B16)

Check with Interest = P*R*T ==>                  \$         75.00   =B12/(B13*B15/B16)      Checks out!!

Step 3: State in Words

From the data presented, we calculated the Rate to be 13.52%.
me

0 days, find the interest rate.

<== Do not have to round
because we are not using this in
any subsequent calculations.
The formatted display of the
number is sufficient.

13.52%.
Find Time Given Interest, Principal, & Rate

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time (in years) = I/(P*R)

Gardenia deposits \$10,000.00 in a savings account at an interest rate of 10.00%. If she earns \$750.00 interest, how many da
the account?

Step 1: List Details:
Interest                                                     \$        750.00
Principal                                                    \$     10,000.00
Rate                                                                  10.00%
Time                                                                            days
Days in a year                                                            360

Step 2: Set up and solve

Time (in years) = I/(P*R) = \$750.00/(\$10,000.00*10.00% =                 0.750 =B12/(B13*B14)
Time in days = 0.75*360 =                                                  270 =B21*B16

Check with Interest = P*R*T ==>                              \$        750.00    =B13*B14*B22/B16

Step 3: State in Words

From the data presented, we calculated the Time to be 270 days.

Find Time Given Interest, Principal, & Rate

Formulas:
Interest = P*R*T
Principal = I/(R*T)
Rate = I/(P*T)
Time I/(P*R)

Gardenia deposits \$10,000.00 in a savings account at an interest rate of 10.00%. If she earns \$750.00 interest, how many mon
the account?

Step 1: List Details:
Interest                                                     \$        750.00
Principal                                                    \$     10,000.00
Rate                                                                  10.00%
Time                                                                            months
Months in a year                                                            12
Step 2: Set up and solve

Time I/(P*R) = \$750.00/(\$10,000.00*10.00% =                          0.750 =B12/(B13*B14)
Time in days = 0.75*12 =                                                 9 =B21*B16

Step 3: State in Words

From the data presented, we calculated the Time to be 9 months.
cipal, & Rate

)

arns \$750.00 interest, how many days did she leave the money in

<== Do not have to round because we
want to use the unrounded decimal to
multiply times the number of days in a
e                       year. (We need the unrounded decimal
so that we get the actual number of
days).

Checks out!!

Time to be 270 days.

cipal, & Rate

rns \$750.00 interest, how many months did she leave the money in
e

Time to be 9 months.
Simple Interest                               >> Face Value or Principal            +
Simple Discount                               >> Proceeds                           +
** The face value and the maturity value are the same for a S. discount note

Bank Discount                                  = Face Value or Maturity Value         *
B                                              = M                                    *

Proceeds                                       = Face Value or Maturity Value         -
P                                              = M                                    -

Example 1:
If you take out a loan with a maturity value (face value) of \$2000 and the bank discount is \$150, what are the
proceeds?

Step 1: List Details:
Face Value or Maturity Value                   =     \$                     2,000.00
Bank Discount                                  =     \$                       150.00

Step 2: Set up and solve

Proceeds                                       = Face Value or Maturity Value         -
P                                              = M                                    -
1,850.00   = \$                    2,000.00        -

Step 3: State in Words

We have to pay back \$2,000.00 and you are going to give us only \$1,850.00?!?

Example 2:
Cynthia Thomas signs an \$8500, 9-month note. If the bank discounts the note at 9%, find the amount of the discount
and proceeds.

Step 1: List Details:
Face Value or Maturity Value                   =                           8,500.00
Time                                           =                                   9 months
Discount Rate (Interest Rate)                  =                              9.00%
Months in the year                             =                                  12

Step 2: Set up and solve

Bank Discount                                  = Face Value or Maturity Value         *
B                                              = M                                    *

Bank Discount = \$8,500.00*09.00%*9/12 =        =                             573.75

Proceeds = 8500-573.75 =                       =                           7,926.25

Step 3: State in Words
After we subtracted the bank discount of \$573.75 from the face value (\$8,500.00) our proceeds were \$7,926.25.
Interest                            Repayment amount
Interest                          = Maturity Value
Bank Discount                     = Face Value or Maturity Value
value are the same for a S. discount note

Discount Rate (Interest Rate)     * Time
D                                 * T

Bank Discount
B

the bank discount is \$150, what are the

Bank Discount
B
\$                      150.00

give us only \$1,850.00?!?

note at 9%, find the amount of the discount

months

Discount Rate (Interest Rate)     * Time
D                                 * T

=ROUND(C33*C35*C34/C36,2)
\$8,500.00) our proceeds were \$7,926.25.
If you know the proceeds you want, how do you figure out the amount to
borrow, the maturity value or face value?

Formula = Maturity Value = Proceeds / (1 - Discount Rate * Time) =
M = P/(1-D*T) =

Example 1:
Mike Modigliani needs \$4000 to buy a machine. Find the amount he needs to
borrow (maturity value) if he plans to repay the note in 180 days and the bank
charges a 12% discount rate.
<== Do not have to
Step 1: List Details:                                     round because we
are not using this in
Proceeds                                               = \$                    4,000.00
any subsequent
Discount Rate (interest Rate)                          =                        12.00%
calculations. The
Time                                                   =                            180 Days       formatted display of
Days in Year                                           =                            360            the number is
sufficient.
Step 2: Set up and solve

M = P/(1-D*T) = \$4,000.00/(1-0.12*180/360)             = \$                    4,255.32      =C9/(1-C10*C11/C12)

Step 3: State in Words

If Mike Modigliani needs \$4,000.00 to buy a machine (proceeds) and the bank is offering him a note due
in 180 days and a bank discount rate of 12%, the face value or maturity value would have to be
\$4,255.32.
<== Do not have to
round because we
are not using this in
any subsequent
calculations. The
formatted display of
the number is
sufficient.

=C9/(1-C10*C11/C12)
Simple Interest Note Simple Discount Note
Face Value                                                        7500                 7500
Interest                                                           225                  225
Amount available to borrower                                      7500                 7275
Maturity value                                                    7725                 7500
Time in days                                                        90                   90
Days in year                                                       360                  360

Effective Interest Rate Simple Interest Note =             0.1200000 =B3/(B2*B6/B7)

Effective Interest Rate Simple Discount Note =            0.12371134 =C3/(C4*C6/C7)

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