1 t r 1 fv c r 18 annuities

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Unformatted text preview: an annuity due calculator, Most problems are ordinary annuities 19 Annuity – Example 6.5 You borrow money TODAY so you need to You compute the present value. compute 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 48 ($24,000) ($24,000) Formula: 1 1− (1.01) 48 PV = 632 .01 = 23,999.54 20 Annuity – Sweepstakes Annuity Example Example Suppose you win the Publishers Clearinghouse Suppose $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today? today? PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29 21 Buying a House You are ready to buy a house and you have $20,000 You 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 income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house? for 22 Buying a House - Continued Bank loan Monthly income = 36,000 / 12 = 3,000 Maximum payment = .28(3,000) = 840 PV = 840[1 – 1/1.005360] / .005 = 140,105 Total Price Closing costs = .04(140,105) = 5,604 Down payment = 20,000 – 5604 = 14,396 Total Price = 140,105 + 14,396 = 154,501 23 Annuities on the Spreadsheet Annuities Example Example The present value and future value The formulas in a spreadsheet include a place for annuity payments place Click on the Excel icon to see an Click example example 24 Quick Quiz – Part II You know the payment amount for a loan and You you want to know how much was borrowed. Do you compute a present value or a future value? value? You want to receive 5,000 per month in You retirement. If you can earn .75% per month and you expect to need the income for 25 years, how much do you need to have in your account at retirement? account 25 Finding the Payment Suppose you want to borrow $20,000 for a new Suppose car. You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). If you take a 4 year loan, what is your monthly payment? monthly 20,000 = C[1 – 1 / 1.006666748] / .0066667 C = 488.26 26 Finding the Payment on a Finding Spreadsheet Spreadsheet Another TVM formula that can be found in a Another spreadsheet is the payment formula spreadsheet PMT(rate,nper,pv,fv) The same sign convention holds as for the PV and The FV formulas FV Click on the Excel icon for an example 27 Finding the Number of Payments Finding – Example 6.6 Example Start with the equation and remember your Start logs. logs. 1,000 = 20(1 – 1/1.015t) / .015 .75 = 1 – 1 / 1.015t 1 / 1.015t = .25 1 / .25 = 1.015t t = lln(1/.25) / ln(1.015) = 93.111 months = 7.76 n(1/.25) years years And this is only if you don’t charge anything And more on the card! more 28 Finding the Number of Payments Finding – Another...
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