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(Present value of complex cash flows) How much do you have to deposit today so that beginning 11 years from now you can withdraw $13,000 a year for the next 4 years (periods 11 through 14) plus an additional amount of $26,000 in the last year (period 14)? Assume an interest rate of 11 percent. * Try again. STEP 1: Picture the problem This investment involves one 4-year, $13,000 ordinary annuity with payments made at the end of years 11 through 14 and one single cash flow 14 years from today. The amount of money you have to deposit today is the sum of the present values of the annuity and the single cash flow. We can use a timeline to identify the cash flows from the investment as follows: Tim Cas The amount of the deposit today equals the sum of the two present values STEP 2: Decide on a solution strategy In this case, we are first trying to determine the present value of an ordinary annuity (PV). We know the annual compound rate (i), the dollar value that is received at the end of each year (PMT), and the number of years the annuity lasts (n). We then compute the present value of the single cash flow by discounting it directly to the present. Once we calculate the present value of all these flows, we can add them together and find their present value. We can find the present value using a mathematical formula, a financial calculator, or an Excel spreadsheet

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