Image Descriptions
4.1
Figure 4.1.1: Timeline showing PV =$1,100 at the Start with an arrow pointing to the end (right) where I = ? when t=5 months. r = 5% annually [Back to Figure 4.1.1]
Figure 4.1.2: Timeline showing PV = ? at the Start with an arrow pointing to the end (right) where I = $2,035 when t=11 months. r = 6% annually [Back to Figure 4.1.2]
Figure 4.1.3: Timeline showing PV =$95,000 at the Start with an arrow pointing to the end (right) where I = $1,187.50 when t=?. r = 5% annually [Back to Figure 4.1.3]
Figure 4.1.4: Calculator Instructions to use the Date Function. Instructions are: 2ND DATE, Down Arrow, DT2 = 9-13-2011, Down Arrow, DBD = 347, Up Arrow, Up Arrow, CPT DT1, DT1 = 10-01-2010 [Back to Figure 4.1.4]
4.2
Figure 4.2.2: Timeline showing PV =$35,000 at Today (on the Left) with an arrow pointing to the end (on the Right) (4 months) where S = ? and r = 4.25% annually [Back to Figure 4.2.2]
Figure 4.2.3: Timeline showing S = $8,000 the end (on the Right) (8 months) with an arrow pointing back to Today (on the Left) where PV =? and r = 4.5% annually. [Back to Figure 4.2.3]
Figure 4.2.E: General Timeline for Equivalent Payments: On the left, “Earlier Date”, “We are trying to find the amount here…”. In the middle, “…at same fair rate of simple interest…”. At the end, “Later Date”, “that is equivalent to some amount over here.” [Back to Figure 4.2.E]
Figure 4.2.5: Timeline showing: On the Left: “Payment due today”, “P = $1,500”. On the Right: “Payment will be made 9 months later”, “S = ?”. r = 5% annually [Back to Figure 4.2.5]
Figure 4.2.6: Timeline showing S1 = $600 at 4 months from today and S2 = $475 at 11 months from today. S1 = $600 moves back to today as P1 = ? and S2 = $475 moves back to today as P2 = ?. At Today, Total Amount Paid (P) = P1 + P2. r = 4.5% annually throughout. [Back to Figure 4.2.6]
4.4
Figure 4.4.0: Timeline showing on the Left, “Date of sale”, “P = ?”, with arrow moving to the end (on the Right) to “Maturity Date” and “S = Face Value”. Yield (r) on the Date of Sale. [Back to Figure 4.6.0]
Figure 4.4.2: Timeline showing “Maturity Date” on the Right with arrow back to the Left to “90 Days Before Maturity (Date of Issue)”. At “Maturity Date”, S = $250,000 moves back to “49 Days After Date of Issue” to P = ? with r = 3.63% annually. [Back to Figure 4.6.2]
Figure 4.4.Y: Timeline showing on the Left, “Date of sale”, “P = Price”. On the Right, “Maturity Date” and “S = Face Value”. in the Middle, “On Date of Sale”, “Yield (r) = ? annually”. [Back to Figure 4.6.Y]
Figure 4.4.3: Timeline showing on the Left, “Issue Date (364 days before maturity)”, “P = $489,027.04”. t = 217 days later to “Date of Sale” and “$496,302.21”. t = 148 days later to “Maturity Date” and “S = $500,000 (Face Value)” on the Right. ra = ? from Issue Date until Date of Sale. rb = ? from Date of Sale to Maturity Date. rc = ? and t = 364 days from Issue Date until Maturity Date. [Back to Figure 4.6.3]
5.2
Figure 5.2.0: Picture of the BAII Plus calculator showing the “Frequency Functions”, and the “Time Value of Money Buttons”.[Back to Figure 5.2.0]
Figure 5.2.1: Timeline showing PV =$35,000 at Today (on the Left) with an arrow pointing to the end (on the Right) (10 years) where FV = ? and 9% quarterly throughout. [Back to Figure 5.2.1]
Figure 5.2.2: Timeline: PV1 = $48,000 at 5 years ago moving to 3.5 years ago at 6% quarterly to become FV1. At 3.5 years ago, FV1 becomes PV2 which moves to 1 year ago at 7% semi-annually to become FV2. At 1 years ago, FV2 becomes PV3 which moves to Today at 7.5% monthly to become FV3 = ?. [Back to Figure 5.2.2]
Figure 5.2.3: Timeline: At 2 years ago, FV1 = $2,000 moves to Today at 6% monthly to become FV1. At Today, there is a$1,500 deposit. At Today, FV1 becomes PV2 which moves to 3 years at 6% monthly to become FV2 = ?. [Back to Figure 5.2.3]
5.3
Figure 5.3.1: Timeline showing PV = ? at Today (on the Left) with an arrow pointing to the end (on the Right) (3 years) where FV = $38,000 and 7.25% monthly throughout. [Back to Figure 5.3.1]
Figure 5.3.2: Timeline: FV1 = $9,200 at 3 years moving back to 2 years at 9% monthly to become PV1. At 22 years, PV1 becomes FV2 which moves to 1 year at 8% quarterly to become PV2. At 1 years, PV2 becomes FV3 which moves to Today at 7 % semi-annually to become PV3 = ?. [Back to Figure 5.3.2]
5.4
Figure 5.4.0: The figure illustrates that two alternative financial streams are equivalent if the total of Payment Stream 1 is equal to the total of Payment Stream 2 on the same focal date. Note that the monies involved in each payment stream can be summed on the focal date because of the fundamental concept of time value of money. [Back to Figure 9.4.0]
Figure 5.4.1: A timeline showing: $1,000 payment at Today moving forward to 6 months (Focal Date) as FV at 6% semi-annually. $1,000 payment at 1 year moving back to 6 months (Focal Date) as PV at 6% semi-annually. At 6 months (Focal Date), FV = $1,030 and PV = $970.87, and the sum of FV and PV is $2000.87. [Back to Figure 9.4.1]
Figure 5.4.2: Timeline: PV1= $4,500 at Today moving to 9 months as FV1. PV2 = $6,300 at 3 months moving to 9 months as FV2. At 9 months, FV = FV1 + FV2 [Back to Figure 9.4.2]
Figure 5.4.3: Original Payment Stream Timeline: $3000 at Today moving to 2 years (Focal Date) as FV1. $2500 at 2.25 years moving back to 2 years as PV1. $4,250 at 3 yeears, 11 months moving back to 2 years as PV2. At 2 years (Focal Date) FV1 + PV1 + PV2 = Total. 9.84% monthly through out. Proposed Payment Stream Timeline: $3,500 at 9 months moved to 2 years (Focal Date) as FV2. x at 2 years. At 2 years (Focal Date), x + FV2 = Total. 9.84% monthly throughout. [Back to Figure 9.4.3]
5.5
Figure 5.5.1: Timeline: PV = $7,100 at Today. FV = $8,615.19 at 3 years. Unknown % quarterly. [Back to Figure 5.5.1]
Figure 5.5.2: Timeline: PV = $15,100 at 5 years ago. FV = $15,000 +$6,799.42 = $21,799.42 at Today. Unknown % monthly. [Back to Figure 5.5.2]
Figure 5.5.3: First Investment Option Timeline: PV to 1 year as FV1 at 2% semi-annually with i=1% and n =2*1=2. FV1 to 2 years as FV2 at 2.5% semi-annually with i=1.25% and n =2*1=2. FV2 to 3 years as FV3 at 3% semi-annually with i=1.5% and n =2*1=2. FV3 to 4 years as FV4 at 3.5% semi-annually with i=1.75% and n =2*1=2. FV4 to 5 years as FV5 at 4.5% semi-annually with i=2.25% and n =2*1=2. Second Investment Option Timeline: PV to 1 year as FV1 at 1% semi-annually with i=0.5% and n =2*1=2. FV1 to 2 years as FV2 at 1.5% semi-annually with i=0.75% and n =2*1=2. FV2 to 3 years as FV3 at 1.75% semi-annually with i=0.875% and n =2*1=2. FV3 to 4 years as FV4 at 3.5% semi-annually with i=1.75% and n =2*1=2. FV4 to 5 years as FV5 at 7% semi-annually with i=3.5% and n =2*1=2. [Back to Figure 5.5.3]
6.1
Figure 6.1.2: Timeline showing PV =$5,000 at Today (on the Left) with an arrow pointing to the end (on the Right) (3 years) where FV = ? and 5% quarterly throughout. [Back to Figure 10.1.2]
Figure 6.1.3: Timeline showing PV1 = $23,500 at 3 years ago moving to 1.75 years ago at 3.8% quarterly to become FV1. At 1.75 years ago, FV1 becomes PV2 which moves to 0.75 year ago at 3.7% quarterly to become FV2. At 0.75 years ago, FV2 becomes PV3 which moves to Today at 3.65% quaterly to become FV3 = ? [Back to Figure 10.1.3]
6.2
Figure 6.2.0: Timeline showing PV = Principal on the Issue Date. PV is brought (at the Nominal Interest Rate of the Note) to the Maturity Date as FV = Maturity Value. The FV at the Maturity Date is then brought back to the Date of Sale as PV = Proceeds of the Sale of the Note (at the Negotiated Discount Rate). Step 1: Draw/label a timeline. Step 2: Calculate FV. Step 3: Calculate PV. [Back to Figure 10.2.0]
Figure 6.2.1: Timeline showing PV = $5,000 on the Issue Date. PV is brought (at 9% monthly) to the 3 years as FV = $6,543.23. The FV at 3 years is then brought back to the Date of Sale (18 months before the maturity date) as PV = ? (Proceeds of the Sale) at 16% quarterly with t=1.5 years. [Back to Figure 10.2.1]
Figure 6.2.2: Timeline showing PV = $6,825 on the Issue Date. PV is brought (at 12% monthly) to 2 years as FV = ?. The FV at 2 years is then brought back to the Date of Sale (6 months before the maturity date) as PV = $7,950.40 (Proceeds of the Sale) at ?% semi-annually with t=0.5 years. [Back to Figure 10.2.2]
Figure 6.2.1: Timeline showing $5,750 moving from today to 72 months (6 years) with i = 6.9%/12 = 0.575% and n = 6 x 12 = 72, giving FV. Then FV from 72 months (6 years) moving back to 45 months (3.75 years) to give PV with n = 27/12 and i = 9.9%/4 = 2.475%. [Back to Figure 10.2.1]
Figure 6.2.2: Timeline showing $36,555 moving from October 15, 2011 to 87 months (7.25 years) with i = 5%/12 = 0.4166666666% and n = 7.25 x 12 = 87, giving FV. Then FV from 87 months (7.25 years) moving back to 57 months (4.75.75 years) to give PV with n = 27/12 and i = ? [Back to Figure 10.2.2]
Figure 6.2.3: Timeline showing $5,750 moving from today to 72 months (6 years) with i = 6.9%/12 = 0.575% and n = 6 x 12 = 72, giving FV. Then FV from 72 months (6 years) moving back to 45 months (3.75 years) to give PV with n = 27/12 and i = 9.9%/4 = 2.475%. [Back to Figure 10.2.3]
6.3
Figure 6.3.1: Timeline showing FV = $15,000 at 19.5 years from today brought back to today using PV and n=19.5 × 2 = 39 [Back to Figure 10.3.1]
Figure 6.3.2a: Timeline showing Issue date of May 29, 2002. FV = $15,000 at Maturity Date of May 29, 2027 brought back to Purchase Date of May 29, 2006 as PV = $2,686.01, with n = 21 × 2 = 42 [Back to Figure 10.3.2a]
Figure 6.3.2b: Timeline showing Issue date of May 29, 2002. FV = $15,000 at Maturity Date of May 29, 2027 brought back to Selling Date of November 29, 2012 as PV = $3,925.28, with n = 14.5 × 2 = 29. [Back to Figure 10.3.2b]
Figure 6.3.2c: Timeline: Issue date of May 29, 2002. FV = $3,925.28 at Selling Date of November 29, 2012 brought back to Purchase Date of May 29, 2006 as PV = $2,686.01, with n = 6.5 × 2 = 13 [Back to Figure 10.3.2c]
7.1
Figure 7.1.1: Timeline showing monthly payments of $81,253.45 at the end of every month from now until 1 year. The FV of sum of all the payments at 1 year is $1,000,000 [Back to Figure 11.1.1]
Figure 7.1.2: Timeline showing quarterly payments of $1000 at the end of every quarter from now until 5 years. The FV of sum of all the payments at 5 years is $20,979.12 [Back to Figure 11.1.2]
Figure 7.1.3: Timeline showing monthly payments of $22.41 at the beginning of every month from now until 2 years. The PV of sum of all the payments at now is $500 [Back to Figure 11.1.3]
7.2 Future Value of Annuities – was 11 in original source
Figure 7.2.1: Timeline showing PV = $0 11 years ago. FV = ? Today. 7.3% quarterly. PMT = $1,000 per quarter (END) [Back to Figure 11.2.1]
Figure 7.2.2: Timeline showning PV = $10,000 Today. FV = ? in 20 years. 9% semi-annually. PMT = $250 per month (END) [Back to Figure 11.2.2]
Figure 7.2.3: Timeline showing PV = $1,000 at Today moving to Year 1 as FV1. Time Segment 1 with 5% semi-annually and PMT = $300 per month (END). FV1 at Year 1 moving to Year 2 as FV2. Time Segment 2 with 6% quarterly and PMT = $1,000 per quarter (END). [Back to Figure 11.2.3]
Figure 7.2.C: BAII Plus Calculator identifying BGN (will appear when in annuity due mode). Exit the Window, Toggle the Setting and Payment Time Button identified. [Back to Figure 11.2.C]
Figure 7.2.4: Timeline showing PV = $0 at Today. FV = ? in 25 years. 5% annually. PMT = $1,000 per week (BGN) [Back to Figure 11.2.4]
Figure 7.2.5: Timeline showing PV = $0 at Today (son is born) moving to Year 5 as FV1. Time Segment 1 with 5.75% monthly and PMT = $1,000 per half year (BGN). FV1 at Year 5 moving to Year 18 as FV2. Time Segment 2 with 5.75% monthly and PMT = $1,000 per quarter (BGN). [Back to Figure 11.2.5]
7.3
Figure 7.3.1: Timeline showing PV = ? at Age 65. FV= $0 at Age 78. 5.1% annually. PMT = $50,000 per year (END) [Back to Figure 11.3.1]
Figure 7.3.2: Timeline showing PV = ? at Age 65. FV= $100,000 at Age 78. 5.1% annually. PMT = $50,000 per year (BGN) [Back to Figure 11.3.2]
Figure 7.3.3: Timeline showing FV = $100,000 at Age 78 moving back to Age 71 as PV1. Time Segment 1 with 5.1% semi-annually and PMT = $60,000 per year (BGN). PV1 at Age 71 moving back to Age 65 as PV2. Time Segment 2 with 5.1% semi-annually and PMT = $50,000 per year (BGN). [Back to Figure 11.3.3]
Figure 7.3.L: Timeline showing Amount of money borrowed (PV) at Day loan taken out moved to Future Date as Future value of the loan (FV1). Interest on the loan throughout. Periodic loan payments (PMT) at END moved to Future date as Future value of the payments (FVord). At Future date, Balance owing with interest (FV1) minus Amount paid with interest (FVord) equals Balance still owing (FV). [Back to Figure 11.3.L]
Figure 7.3.4: Timeline: PV = $71,482.08 – $5,000 (down payment) = $66,482.08 loan at 2 years ago moved to Today as FV1 (Future Value of the Loan). 5.9% monthly throughout. PMT = $1,282.20 per month (END) moved to Today as Future value of the payments (FVord). At Future date, Balance owing with interest (FV1) minus Amount paid with interest (FVord) equals Balance still owing (FV). [Back to Figure 11.3.4]
Figure 7.3.PVL: Timeline showing PV = ? at Date of Loan Contract Sale. Interest on the loan throughout. Adjusted last payment at End of Loan Contract moved back to Date of Loan Contract Sale as PV1 (using negotiated interest rate as your discount rate). Periodic loan payments (PMT) at END moved back to Date of Loan Contract Sale as PVord (using as Future value of the payments (FVord) (using negotiated interest rate as your discount rate). At Date of Loan Contract Sale, PV of annuity payments (PVord) minus PV of last payment (PV1) equals Total PV (Proceeds of sale). [Back to Figure 11.3.PVL]
Figure 7.3.5: Timeline showing PV = ? at 2 years after start of loan. Interest at 10.8% semi-annually loan throughout. Final payment = $1,282.49 at 5 years after the start of loan moved back to 2 years after the start of the loan as PV1. PMT = $1,282.20 per month (END) moved back to 2 years after start of loan as PVord. At 2 years after start of loan, PV of annuity payments (PVord) minus PV of last payment (PV1) equals Total PV (Proceeds of sale). [Back to Figure 11.3.5]
7.4
Figure 7.4.1: Timeline showing PV = $25,000 at Today and FV = $0 at 3 Years. 7.8% monthly. PMT = ? per month (END) [Back to Figure 11.4.1]
Figure 7.4.2: Timeline showing PV = $10,000 at Today and FV= $0 at 1 Year. 5.25% quarterly. PMT = ? per month (BGN) [Back to Figure 11.4.2]
Figure 7.4.3: Timeline showing PV = $10,000 at Age 22 and FV= $1,700,000 at Age 65. 9% annually. PMT = ? per month (BGN) [Back to Figure 11.4.3]
Figure 7.4.4.: Timeline showing PV = $1,000,000 at Today and FV= $10,000,000 at 5 Years. 6.15% semi-annually. PMT = ? per six months (END) [Back to Figure 11.4.4]
7.6
Figure 7.6.1: Timeline showing PV = $399 at Today and FV= $0 at 1 year. ?% annually. PMT = $59.88 per month (BGN) [Back to Figure 11.6.1]
Figure 7.6.2: Timeline showing PV = $0 at Today and FV= $550,000 at 4 years. Nominal= ? % quaterly. Effective = ? % annually. PMT = $30,000 per quarter (END) [Back to Figure 11.6.2]
Figure 7.6.3: Timeline showing PV = $5,000 at Today and FV= $100,000 at 14 years. ?% annually. PMT = $250 per month (BGN) [Back to Figure 11.6.3]
Figure 7.6.4: Timeline showing PV = $54,904.64 at Today and FV= $30,000 (still owing) at 2 years. ?% annually. PMT = $250 per month (END) [Back to Figure 11.6.4]
8.1
Figure 8.1.0: Timeline showing a Single Payment Invested at Start and a Deferral Period (Accummulation Stage) from Start to Years. At Years, Maturity Amount of Single Payment = Principal of Annuity. From Years to End of Annuity (Years), Payment Stage with PMT (annuity type). At End of Annuity (Years), FV = $0 [Back to Figure 12.1.0]
Figure 8.1.1: Timeline showing at Age 80, FV = $0. From Age 80, FV is brought back to Age 65 as PVord. From Age 80 to Age 65 (Payment Stage), 5% annually and PMT = $5,000 per month (END). Deferral Period (Accummulation Stage) from Age 33 to Age 65 with 9% annually. [Back to Figure 12.1.1]
Figure 8.1.2: Timeline showing at 10 Years after Deferral Period, FV = $0. From 10 Years after Deferral Period, FV is brought back to end of Deferral Period as PVdue. From 10 Years after Deferral Period to End of Deferral Period (Payment Stage), 4.3% semi-annually and PMT = $2,500 per month (BGN). Deferral Period (Accummulation Stage) from Start to End of Deferral Period with 8.25% quarterly. At Start, PV = $50,000. [Back to Figure 12.1.2]
Figure 8.2.3: Timeline: At Birth, PV = $3,000. From Birth to Age 18 (Deferral Period =Accumulation Stage) with 6% monthly. PV at Birth moves to Age 18 as PVord = FV (after deferral). From Age 18 to Age 23 is the Payment Stage with 4.5% quaterly and PMT = ? per quarter (END). At Age 23, FV = $0. [Back to Figure 12.1.3]
Figure 8.1.4: Timeline: Today, PV = $25,000. From Today to 14 years (Deferral Period =Accumulation Stage) with 8% annually. PV at today moves to 14 Years as PVdue= FV (after deferral). From 14 Years to is the Payment Stage with 3.25% semi-annually and PMT = 2,3000 per month (BGN). At ? (after the deferral period), FV = $0. [Back to Figure 12.1.4]
