VIEWS: 373 PAGES: 60 CATEGORY: Personal Finance POSTED ON: 7/6/2010 Public Domain
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% Type of Note Amount Received 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. Type of Note Amount Received 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)