SOLUTION: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year,

Question 1151380: Ishan and Hazel plan to retire at age 60 with a retirement income of $48,000 a year from their savings. Rather than pay themselves the whole amount at the beginning of each year, they have decided that payment at the beginning of each quarter of $12,000 gives them the right balance of flexibility and maximized interest earnings. They feel they can safely earn an interest rate of 8%, compounded quarterly, on their money and they are budgeting based on the prediction that they will live until they are 90 years old.
How much money will they have to have saved by the time they are 60 in order to reach their retirement goal? [1]
If the same total calculated above was to be saved, but no interest earned whatsoever, how much would be available to live on each quarter? [2]
If the full 30 years are lived and quarterly budget spent, how much money in total will have been utilized in retirement? [3]
How much will have been earned in interest? [4]
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.


It works in this way:  they withdraw $12000 at the beginning of every quarter, and the account is compounded quarterly 
at the nominal rate of 8% per year.


The general formula  to calculate the starting amount at the account is

    X = .


In this formula, W is  the regular withdrawal per quarter, W = $12000;  the factual quarterly compounding rate 
is  r = 0.08/4 = 0.02,  p = 1 + 0.02 = 1.02, and the number of payment periods  is n = 30 years * 4 quarters = 120. So


          X =  = 555,149.96 dollars.     It is the  ANSWER  to the problem's question [1].


The answer to question [2] is   = 0.39 dollars.


The answer to question [3] is 30*4*12000 = 1,440,000 dollars.


Regarding question [4], I do not understand precisely its meaning.

Solved.

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See my lessons in this site associated with annuity saving plans and retirement plans

    - Ordinary Annuity saving plans and geometric progressions
    - Annuity Due saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
    - Withdrawing a certain amount of money periodically from a compounded saving account (*)
    - Miscellaneous problems on retirement plans

and especially lesson marked (*) in the list as the most relevant to the given problem.

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