SOLUTION: Suppose you want to have $800,000 for retirement in 30 years. Your account earns 8% interest. a) How much would you need to deposit in the account each month? $ b) How m

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Question 1122484: Suppose you want to have $800,000 for retirement in 30 years. Your account earns 8% interest.
a) How much would you need to deposit in the account each month?
$

b) How much interest will you earn?
$
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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Suppose you want to have $800,000 for retirement in 30 years. Your account earns 8% interest.
a) How much would you need to deposit in the account each month?
$

b) How much interest will you earn?
$
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To be consistent, the condition should be edited in this way: 

    Suppose you want to have $800,000 for retirement in 30 years. Your account is compounded monthly and earns 8% annual interest.


Then the solution is THIS : 

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29,    


where  FV is the future value of the account;  P is the monthly payment (deposit); r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


From this formula, you get for the monthly payment 


    P = FV%2A%28r%2F%28%281%2Br%29%5En-1%29%29.     (1)


Under the given conditions, FV = $800,000;  r = 0.08/12;  n = 30*12.  So, according to the formula (1), the monthly payment is


    P = 800000%2A%28%28%280.08%2F12%29%29%2F%28%281%2B0.08%2F12%29%5E%2830%2A12%29-1%29%29%29 = $536.78.


Answer.  a)  How much would you need to deposit in the account each month ? - $536.78.


            Note that of projected $800,000 the total you deposit will be only  30*12 times $536.78, i.e. about 30*12*536.78 = 193241 dollars.                     
            The rest is what the account will earn/accumulate in 30 years.


         b)  How much interest will you earn ?  - You will earn %28%28800000-193241%29%2F193241%29%2A100 = 314%  of interest.

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On Ordinary Annuity saving plans,  see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.