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History Bookmarks People Window Help ttps://edugen willeyplus.com/ed Would you like to translate ir? Nope Translate Never translate Arabic Options Return to Blackboard PRINTER VERSION ·BACK Brief Exercise 6-10 Newman Quincy wants to withdraw $31,700 each year for 15 years from a fund that earns 11% interest. How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately? (Round factor values to S decimal places, e.g. 1.25124 and final answers to O decimal places, e.g. 458,581.) First withdrawal at year-end First withdrawal immediately Question Attempts: 0 of 3 used SAVE FOR LATER SUBKIT ANSWER 4 MacBook Air

Explanation / Answer

Answer 1 Using Present value of annuity formula , we can calculate the investment needed today if first withdrawal is at year end Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = Investment needed today = ? P = Withdrawal at evey year end = $31700 r = rate of interest per year = 11% n = no.of years = 15 Present value of annuity = 31700 x {[1 - (1+0.11)^-15]/0.11} Present value of annuity = 31700 x 7.19087 Present value of annuity = 227950.57 Amount investment needed if first withdrawal is at year end = $2,27,951 Answer 2 Using Present value of annuity due formula , we can calculate the investment needed today if first withdrawal is immediate. Present value of annuity due = P + P x {[1 - (1+r)^-(n-1)]/r} Present value of annuity = Investment needed today = ? P = Yearly withdrawal = $31700 r = rate of interest per year = 11% n = no.of years = 15 Present value of annuity due = 31700 + 31700 x {[1 - (1+0.11)^-(15-1)]/0.11} Present value of annuity due = 31700 + 31700 x 6.981865 Present value of annuity due = 31700 + 221325.13 Present value of annuity due = 253025.13 Amount investment needed if first withdrawal take place immediately = $2,53,025

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