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All Rights ReservedChapter 21 Time Value of Money Chapter 5 Future and Present Values Loan Amortization, Annuities Financial Calculator

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All Rights ReservedChapter 22 Time Value of Money I.Four Critical Formulas A.Future Value: value tomorrow of $1 invested today. B.Present Value: value today of $1 to be received tomorrow. C.Future Value of an Annuity: value several periods from now of a stream of $1 investments. D.Present Value of an Annuity: value today of a stream of $1 payments to be received for a set number of future periods.

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All Rights ReservedChapter 23 Important TVM Concepts A. Future Value 1. What $1 invested today should grow to over time at an interest rate i. 2. FV = future value, P = principal, i = int. rate. a. I = interest (dollar amount), I = P i 3. Single interest: FV = P + I = P + P(i) = P(1+i) 4. Multiple Interest Periods: FV i,n = P (1+i) n b. (1+i) n = Future Value Interest Factor c. FV i,n = P FVIF i,n

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All Rights ReservedChapter 24 Important TVM Concepts B. Present Value; 1.The value today of $1 to be received tomorrow. 2.Solving the Future Value Equation for PV; a. PV = FV (1+i) single period discounting. b. PV = FV (1+i) n multi-period discounting. c. PV = FV (1+i) -n common form. d. (1+i) -n = Present Value Interest Factor. e. PVIF = 1 / FVIF (and vice-versa for same i, n)

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All Rights ReservedChapter 25 Important TVM Concepts C.Future Value of an Annuity (FVA) e.g. Retirement Funds: IRA, 401(k), Keough 1. A series of equal deposits (contributions) over some length of time. 2. Contributions are invested in financial securities; stocks, bonds, or mutual funds. 3. The future value of accumulation is a function of the number and magnitude of contributions, reinvested interest, dividends, and undistributed capital gains. FVA = PMT * FVIFA

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All Rights ReservedChapter 26 Important TVM Concepts D.Present Value of an Annuity (PVA) 1.Insurance Annuities a. Provide recipient with a regular income (PMT) for a set period of time. b.The present value (PV) of the payments to be received is the price of the insurance annuity. c.PVA = PMT * PVIFA 2. Types of Annuities: a. Ordinary Annuity: payments received at end-of-period. b. Annuity Due: payments received at beginning-of- period

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All Rights ReservedChapter 27 Important TVM Concepts 3.Annuitize Investment Accumulations a.We have accumulated a sum of money and now desire to begin a series of [N] regular payouts: e.g. monthly checks b.We assume accumulated funds will continue to earn some rate of return (I/YR) c.The accumulation is treated as the present value (PV). d.How much income (PMT) will a certain accumulated amount produce?

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All Rights ReservedChapter 28 Computing FVA A.FVA formula: 1. FVA = P ([(1+i) n - 1] i) = P FVIFA [(1+i) n - 1] i = future value interest factor for an annuity or FVIFA i,n. annuity or FVIFA i,n. 1. Assumption; steady return rate over time and equal dollar amount contributions.

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All Rights ReservedChapter 29 Computing PVA A.PVA formula: 1. PVA = P ([1 - (1+i) -n ] i) = P PVIFA [1 - (1+i) -n ] i = present value interest factor for an annuity or PVIFA i,n. annuity or PVIFA i,n. 1. Assumption; constant return rate over time and equal dollar amount distributions.

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All Rights ReservedChapter 210 Current Law A. Traditional and Roth IRAs Contribution limits for Traditional and Roth IRAs will rise from $2000 to $5,000 between 2002 and 2008. After 2008, the limit may be adjusted annually for inflation. Tax YearLimit 2002-2004 $3,000 2005-2006$4,000 2008$5,000 2009-2010Indexed to Inflation

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All Rights ReservedChapter 211 Current Law B. 401(k), 403(b), and 457 Plans These limits are on pretax contributions to certain employer- sponsored retirement plans. Remember that employers have the option of imposing lower limits than the government maximums, which will rise to $15,000 by 2006. Tax Year Limit 2002$11,000 2003$12,000 2004$13,000 2005$14,000 2006$15,000 2007-2010Indexed to Inflation

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All Rights ReservedChapter 212 Sample IRA Problem A.Suppose you want to know how much an IRA (individual retirement account) plan will grow to if you deposit $5,000 per year (the maximum under current law) or $416.67 per month every month for the next 20 years or 240 monthly deposits. Well assume monthly compounded interest and annual rate of 7 percent (7% per annum). B.What is the Future Value of the Accumulation (FVA)?

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All Rights ReservedChapter 213 Future Value of an Accumulation 1. Clear the TVM registers; BAII+: press [2nd], then [FV] (CLR TVM) HP10B: press [YK] [INPUT] (CLEAR ALL ) 2. Set the Periods per year register BAII+: Press [2nd] [I/Y] for the P/Y function; enter 12, then press [ENTER] [2 nd ] [CPT] to QUIT this subroutine. HP10B: enter 12, press [YK] [PMT] (P/YR)

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All Rights ReservedChapter 214 Future Value of an Accumulation 3. Enter 240, press [N]. 4. Enter 7, press [I/Y]; interest rate per annum. 5. Enter 416.67, then [+/-] and then [PMT]. 6. BAII+: Press [CPT] then [FV]; 217,054.51 (display) HP10B: Press [FV]: 217,054.51 display (display) Don't clear the values yet. We're going to use them in the next problem.

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All Rights ReservedChapter 215 Future Value of an Accumulation A.What effect does an extra 10 years of $416.67 deposited per month have on the FVA? The FVA after 30 years of monthly savings... a.BAII+: Enter 360, press [N] Press [CPT] [FV]; $508,325.31 (display) HP10B: enter 360, press [N] Press [FV]: $508,325.31 (display) b. =c. The total deposits are 416.67 * 360 = $150,001.20. The other $358,324.11 is the accumulated interest.

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All Rights ReservedChapter 216 Future Value of an Accumulation 1.What effect does the rate of return have on the size of the accumulation? Suppose the interest rate was 12%, what is the FVA? a. Enter 12, press [I/Y]. b. BAII+: Press [CPT] [FV]; $1,456,246.71 HP10B: Press [FV]: $ 1,456,246.71 HP10B: Press [FV]: $ 1,456,246.71 2. The FVA if we assume 30 years of monthly deposits of 416.67 accumulating at 12% per annum compounded monthly.

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All Rights ReservedChapter 217 Tax-Deferred Retirement Savings B. Other Types of Retirement Savings Plans; 1. 401(k) plans; company and individual contributions. 2. 403(b) plans; used by non-profit organizations. 3. Simple plans; plans fore the self-employed. 4. Keough Plans; for professionals such as doctors and lawyers.

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All Rights ReservedChapter 218 ANNUITIZING ACCUMULATIONS A. Annuitizing Pension Fund Accumulations; 1.In the last problem, we accumulated $1,456,246.71 over a 30-year period with monthly contributions to an IRA. We assumed a monthly compounded rate of return of 12% per annum. Current tax law permits the annuitization of IRAs and other similar plans at age 59 years and 6 months. 2.Annuitization of plans must commence when a person reaches 70 years and 6 months. For RMD; http://www.ira.com/faq/faq-54.htm 3.Annuitizing an accumulation is the reverse process. Now instead of paying into the retirement plan, the plan will make payments to you.

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All Rights ReservedChapter 219 ANNUITIZING ACCUMULATIONS B.Suppose we use the $1,456,246.71 to buy a "single payment" ordinary annuity which will guarantee a 7% rate of return P.A. for 25-years. How much will the monthly payment be? 1.(Well ignore the fee-premium for the annuity for the time being.)

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All Rights ReservedChapter 220 ANNUITIZING ACCUMULATIONS A.Calculating Monthly Payout 1. Clear TVM registers: BAII+: [2 nd ] [FV] (CLR TVM) HP10B; [YK] [INPUT] (CLEAR ALL) 2. Enter 300 and press [N] key. 3. Enter 7 and press [I/Y] key. 4. Enter 1456246.71. Press [+/-], then [PV]. 5. BAII+: Press [CPT] key then [PMT] HP10B: Press [PMT] 10,292.45 (display) HP10B: Press [PMT] 10,292.45 (display) 7. Total payout over 25 years = $10,292.45 * 300 = $3,087,734.63. (all this from a $150,000 investment)

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All Rights ReservedChapter 221 ORDINARY ANNUITIES A. Calculating the Price of an Insurance Annuity [Policy] using the BA II Plus 1.Suppose we desire to collect $5,000 per month for 20 years (240 payments) and the rate of return is 9% compounded monthly. 2.How much must we pay for an annuity contract that will pay 5,000 per month for 20 years?

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All Rights ReservedChapter 222 ORDINARY ANNUITIES B.Calculating the Price an Insurance Annuity [Policy] using Financial Calculator; 1. Clear the TVM registers. 2. Enter 240 and press [N]. 3. Enter 9 and press [I/Y]. 4. Enter 5000 and press [PMT]. 5. Press [CPT] and [PV] or [PV] 6. Display should show; -555,724.77 $555,724.77 is the price of annuity. The negative sign reminds us that this is a price (negative cash flow). $555,724.77 is the price of annuity. The negative sign reminds us that this is a price (negative cash flow).

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All Rights ReservedChapter 223 Total Returns

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All Rights ReservedChapter 224 INVESTMENT RETURNS

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All Rights ReservedChapter 225 LOAN REPAYMENTS A.How much will the monthly payments for a $23,000 car loan be if the per annum rate is 4.75% for 60 months. (SECU payroll-deduct or 5.25% direct pay)? We'll solve this problem using the BAII+. 1. Clear the TVM registers. 2. Check the values set for P/Y (=12). 3. Enter 60, press [N]. 4. Enter 4.75, press [I/YR]. 5. Enter 23000, press [PV]. 6. BAII+: Press [CPT] [PMT]; PMT = -431.41 (display) $436.68 (if direct pay at 5.25%)

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All Rights ReservedChapter 226 MORTGAGE LOANS A.How much will the monthly payments for a $160,000 loan be if the per annum rate is 4.75% and the term is 30 years (360 months)? 1. Clear the TVM registers. 2. Check the values set for P/Y (=12). 3. Enter 360, press [N]. 4. Enter 4.75, press [I/YR]. 5. Enter 160,000, press [PV]; $160,000 mortgage loan. 6. BAII+: Press [CPT] [PMT]; PMT = -834.64 (display) Leave these values in the calculator. Well use them to compute the amortization schedule.

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All Rights ReservedChapter 227 MORTAGE AMORTIZATION A.All loans are amortized over their life. Each payment includes an interest portion and a principle portion. The BAII+ computes amortization schedules using the AMORT function. BAII+: [2 ND ] [PV] BAII+: [2 ND ] [PV]

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All Rights ReservedChapter 228 MORTAGE AMORTIZATION A.BAII+ (12 month totals) 1.Press [2nd] [PV]: P1 = 1.00 (display) 2.Press [ ]: P2 = 1 or 12.00 (display) a.If P2 = 1.00 then enter 12, [ENTER]: P2 = 12.00 3.Press [ ]: BAL = 157,531.03 4.Press [ ]: PRN = -2,468.97 5.Press [ ]: INT = -7,546.71 6.Press [ ]: then press [CPT]: P1 = 13.00 7.Press [ ]: P2 = 24.00 (continue [ ] for values)

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All Rights ReservedChapter 229 HOMEWORK CHAPTER 5 A.Selt-Test: ST-1, parts c, f, i, j B.Questions: 5-3, 5-4, 5-6 C.Problems: 5-1, 5-2, 5-3, 5-4, 5-5

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