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ator ? Another way to use the financial calculator for uneven cash flows is to use the cash flow keys – Texas Instruments BAII Plus ? Press CF and enter the cash flows beginning with year 0. ? You have to press the “Enter” key for each cash flow ? Use the down arrow key to move to the next cash flow ? The “F” is the number of times a given cash flow occurs in consecutive years ? Use the NPV key to pute the present value by entering the interest rate for I, pressing the down arrow and then pute ? Clear the cash flow keys by pressing CF and then CLR Work McGrawHill/Irwin 169。 CF0 = 0。 F01 = 1。 F02 = 1 ? NPV。 CPT NPV = – No – the broker is charging more than you would be willing to pay. McGrawHill/Irwin 169。 CF0 = 0。 F01 = 39。 F02 = 5。 I = 12。 2022 The McGrawHill Companies, Inc. All rights reserved. Saving For Retirement Timeline 0 1 2 … 39 40 41 42 43 44 0 0 0 … 0 25K 25K 25K 25K 25K Notice that the year 0 cash flow = 0 (CF0 = 0) The cash flows years 1 – 39 are 0 (C01 = 0。 F02 = 5) McGrawHill/Irwin 169。 Years 2 and 3 CFs = $200。 2022 The McGrawHill Companies, Inc. All rights reserved. Annuities and Perpetuities Defined ? Annuity – finite series of equal payments that occur at regular intervals – If the first payment occurs at the end of the period, it is called an ordinary annuity – If the first payment occurs at the beginning of the period, it is called an annuity due ? Perpetuity – infinite series of equal payments McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Annuities and the Calculator ? You can use the PMT key on the calculator for the equal payment ? The sign convention still holds ? Ordinary annuity versus annuity due – You can switch your calculator between the two types by using the 2nd BGN 2nd Set on the TI BAII Plus – If you see “BGN” or “Begin” in the display of your calculator, you have it set for an annuity due – Most problems are ordinary annuities McGrawHill/Irwin 169。 1 I/Y。 CPT PV = 23, ($24,000) ? Formula: ,2301.)(1163248????????????? ??PVMcGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Buying a House ? You are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly ine. The interest rate on the loan is 6% per year with monthly pounding (.5% per month) for a 30year fixed rate loan. How much money will the bank loan you? How much can you offer for the house? McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Annuities on the Spreadsheet Example ? The present value and future value formulas in a spreadsheet include a place for annuity payments ? Click on the Excel icon to see an example McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Finding the Payment ? Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, pounded monthly (8/12 = .66667% per month). If you take a 4 year loan, what is your monthly payment? – 20,000 = C[1 – 1 / ] / .0066667 – C = McGrawHill/Irwin 169。 2022 The McGrawHill Companies, Inc. All rights reserved. Finding the Number of Payments – Example ? Start with the equation and remember your logs. – 1000 = 20(1 – 1/) / .015 – .75 = 1 – 1 / – 1 / = .25 – 1 / .25 = – t = ln(1/.25) / ln() = months = years ? And this is only if you don’t charge anything more on the card! McGrawHill