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Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of $14500 (starting on December 25, 2016) from his savings account to supplement his income and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits into the savings account starting on December 25, 2000 and ending on December 25, 2015. If the savings account pays interest at 7.3% annually, how large should Ralph's deposits be in order for him to realize his goal?

First off I discount to find how much he will need in 15 years to withdraw that 14500 for 10 years

A = 14500((1-(1.073)^-10)/(.073)) A = 100 444.5089

Shouldn't the annual payments simply be

100444.5089 = PMT((1.073^15)-1)/.073

Although PMT = 3 905.70 is not giving me the correct answer

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  • $\begingroup$ Have you set up a timeline? Set the accumulated value of the deposit annuity to the present value of the withdrawal annuity $\endgroup$
    – user224997
    Feb 3 '17 at 21:19
  • $\begingroup$ Yes I set to use the focal date at 15 years in, found that he needs 100444.51 dollars, so he would need to deposit 3905.70 per year, but that answer I am getting is incorrect. $\endgroup$ Feb 3 '17 at 21:25
  • $\begingroup$ You have to use a-angle and s-angle formulas, or their "due" forms because there is a series of deposits and then a series of withdrawals $\endgroup$
    – user224997
    Feb 3 '17 at 21:28
  • $\begingroup$ I'm confused by what you mean by that, could you show it in more depth? $\endgroup$ Feb 3 '17 at 21:29
  • $\begingroup$ @AlexVincent I´m back and I´m too late. As I said you got help in a short time. $\endgroup$ Feb 3 '17 at 22:35
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PMT((1.073)^16-1)/.073)=14500((1-v^10)/.073) PMT=3512.687

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  • $\begingroup$ v=1/1.073 the present value factor $\endgroup$
    – user224997
    Feb 3 '17 at 21:35
  • $\begingroup$ That's the right answer, looks like I was using 15 years instead of 16. Thank you $\endgroup$ Feb 3 '17 at 21:40

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