SOLUTION: Suppose you want to have $300,000 for retirement in 20 years. Your account earns 5% interest. How much would you need to deposit in the account each month?

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Question 1160115: Suppose you want to have $300,000 for retirement in 20 years. Your account earns 5% interest. How much would you need to deposit in the account each month?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

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 = $300,000;  r = 0.05/12;  n = 20*12 = 240.  
So, according to the formula (1), you get for the monthly payment 


    P = 300000%2A%28%28%280.05%2F12%29%29%2F%28%281%2B0.05%2F12%29%5E240-1%29%29 = $729.87.


Answer.  The necessary monthly deposit value is $729.87.


Note that of projected $300,000, the total of your deposits will be only  20*12 times $729.87, 
i.e.  20*12*729.87 = 175169 dollars. The rest is what the account will earn/accumulate in 20 years.

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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.

The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.

When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.