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Session 4 Present Value Annuity Due Serial Payment Future Sum Amortization

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## Session 4 Present Value Annuity Due Serial Payment Future Sum Amortization

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**CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL**EDUCATION PROGRAMFinancial Planning Process & Insurance Session 4 Present Value Annuity Due Serial Payment Future Sum Amortization**PV of a Serial Payment**When Kim retires in 15 years, she wants to receive the equivalent of a retirement income of $50,000 at the beginning of each year. She also wants the income to adjust annually for inflation. Kim believes that inflation will average 4% and that she can earn 7% on her investments. Assuming she wants to plan for 25 yearsof retirement, and she just received a sizable settlement from an auto accident she was in, how much will Kim need to invest today in order to provide the desired income?**Three Steps of Present Value Serial Payment Process**PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG) • Inflate One Payment Rate of Inflation Today Future Discount Step 2 ResultDiscount (Investment) Rate**Step 1: PV of a Serial Payment**HP10BII/10BII+ PV +/– 50,000 4 I/YR N 15 FV = Answer 1: $90,047 (Becomes the PMT in Step 2)**Step 2: PV of a Serial Payment**HP10BII/10BII+ Set to [BEGIN] mode – 1.07 1 1.04 100 I/YR = +/– PMT 90,047 N 25 PV = 2.8846 Answer 2: $1,634,171 (Becomes the FV in Step 3)**Shortcut to Calculate Inflation-Adjusted Interest Rate**The following steps relate a shortcut method for arriving at the inflation-adjusted interest rate. To do this calculation on the calculator (assuming a 4% inflation rate and a 7% investment return) use the following keystrokes: • Enter 1 plus the inflation rate (e.g. 1.04) • Press the INPUT key • Then enter 1 plus the interest rate (e.g. 1.07) • Press the [orange SHIFT] key • Then press the percent change key • Your answer should be on the calculator screen as 2.8846**Step 3: PV of a Serial Payment**HP10BII/10BII+ FV 1,634,171 +/– I/YR 7 15 PV N = Final Answer: $592,300**Three Steps of Present Value Serial Payment Process**PVAD Serial PMT Calculation Inflation-Adjusted Rate (BEG) • Inflate One Payment Rate of InflationPV=$50,000I/YR= 4N = 15FV = $90,047 (becomes PMT) PMT=$90,047 PMT = $90,047 PMT = $90,047 Today Future N = 25 I/YR = ([1.07/1.04] 1)×100 IAIR = 2.8846PMT= 90,047 I/YR = 2.8846 N = 25 PV = $1,634,171 (Begin Mode) Discount Step 2 ResultDiscount (Investment) RateFV = $1,634,171N = 15I/YR = 7PV = $592,300**Serial Payment For A Future Sum**Today 1st Serial Payment Future Delay of 1 Period To begin saving… Inflation Adjustment**Example of Serial Payment of a Future Sum**Mark Blevins, your client wants to retire in 5 years: • In today’s dollars, he’ll need $100,000 at that time. • Inflation will average 4% over the long run. • Annual after-tax return on investments is 7%. You need to determine a series of inflating payment amounts that will add up to $121,665 in five years: • Future value of $100,000 inflated 4% annually for 5 years is $121,665.29 (payment amounts are not known). • Enter desired lump sum of $100,000 (i.e., stated in today’s dollars) as Future Value. These steps on a financial calculator are identical to those for payment for an ordinary annuity, except that here the inflation- adjusted interest rate is used to calculate initial payment.**Calculation of Serial Payment of a Future Sum**1 2 3 4 5 0 FV $ 25,736.31 $19,634.11 ×1.04 = 25,014.74 $20,419.48 ×1.04 = 24,313.39 $21,236.26 ×1.04 = $22,085.71 ×1.04 = 23,631.71 22,969.14 $ 121,665.29 HP10BII/10BII+ This calculation determines: • Serial payment to be made each year • Based on the effect of inflation • Amount payments will grow • Total amount will be attained 100 1.07 1.04 – 1 Each sum is invested at 7% = I/YR 2.8846 equaling 100,000 FV 5 N PMT = $18,879 1.04 PMT = Answer: $19,634 Serial payment at the end of the first year.**Amortization**• Amortization is the process of liquidating a debt by making installment payments. • Amortization calculations are done to divide a series of payments, into amounts that applies to interest and principal. • The amortization process involves two sets of calculations: • the first step calculates the periodic payment; • the second step identifies the interest and principal amounts.**Amortization Calculation**In the process of assisting Barney and Betty to calculate what they still owe on their home, you are provided with the following information: They purchased their home 8 years ago for $239,500. They made a 20% down payment, and financed the balance using a 30-year mortgage with a 5.15% interest rate. Taxes and insurance increase the payment by $300 per month. In the process of calculation you tell them that they have an outstanding principal balance of what amount? • $129,524 • $164,365 • $165,071 • $206,338**Amortization Solution (1)**• Set the calculator for 12 p/yr. • End Mode. • 20% down payment is $47,900 • Balance financed of $191,600 as the PV • Calculate the regular monthly payment: • N = 360 (or 30 years times 12 months per year). • I/YR = 5.15 • Calculate the payment or PMT = $1,046.19**Amortization Solution (2)**• In calculating 8 years of payments, we are examining the results of 96 payment periods or 8 times 12 = 96; • To accomplish this we must press the following keys: • 1 [INPUT]; • 96 [SHIFT], • [AMORT] look under the FV key for AMORT. • Once this has all been done the following should be on your screen 1 – 96. • Then push the [=] key and the principal paid thus far in 8 years will show up; press the [=] key again and interest paid to date shows up. • Press [=] key one more time and the remaining principal balance will be displayed.**CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL**EDUCATION PROGRAMFinancial Planning Process & Insurance Session 4End of Slides