SOLUTION: Xiao Li wishes to accumulate​ $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her​ i

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Question 1124738: Xiao Li wishes to accumulate​ $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her​ investments, how much must she deposit at the end of each​ year?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

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


    FV = ,   


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


From this formula, you get for for the annual payment 


    P = .     (1)


Under the given conditions, FV = $50,000;  r = 0.05;  n = 10.  So, according to the formula (1), you get for the annual payment 


    P =  = $3975.23.


Answer.  The necessary annual deposit value is $3975.23.


Note that of projected $50,000 the total of Xiao Li's deposits will be only  10 times $3975.23, i.e. 39,752.30 dollars.
The rest is what the account will earn/accumulate/accrue in 10 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.


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