SOLUTION: QUESTION 1 A new mother would like to start a college fund for her newborn daughter. She makes quarterly deposits of $500 into a college fund that earns 6% compounded quarterly

Algebra ->  Finance -> SOLUTION: QUESTION 1 A new mother would like to start a college fund for her newborn daughter. She makes quarterly deposits of $500 into a college fund that earns 6% compounded quarterly      Log On


   

Question 1186136: QUESTION 1
A new mother would like to start a college fund for her newborn daughter. She makes quarterly deposits of $500 into a college fund that earns 6% compounded quarterly for the next 18 years.
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How much will her daughter have available in her college fund when she turns 18? $
Round to the nearest dollar
What is total amount the mother deposited into the fund over the 18 years? $
Round to the nearest dollar
How much interest was earned over the 18 years? $
Round to the nearest dollar
Use the WHOLE DOLLAR AMOUNTS you entered in as your answers above.
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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A new mother would like to start a college fund for her newborn daughter. She makes quarterly deposits
of $500 into a college fund that earns 6% compounded quarterly for the next 18 years.
.
How much will her daughter have available in her college fund when she turns 18? $
Round to the nearest dollar
What is total amount the mother deposited into the fund over the 18 years? $
Round to the nearest dollar
How much interest was earned over the 18 years? $
Round to the nearest dollar
Use the WHOLE DOLLAR AMOUNTS you entered in as your answers above.
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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,    (1)


where  FV is the future value of the account;  P is the quarterly payment (deposit); 
r is the quarterly effective percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 500;  r = 0.06/4;  n = 4*18 = 72.  
So, according to the formula (1), she will get at the end of the 18-th year


    FV = 500%2A%28%28%281%2B0.06%2F4%29%5E%284%2A18%29-1%29%2F%28%280.06%2F4%29%29%29 = 500%2A%28%281.015%5E72-1%29%2F0.015%29 = $64038   (rounded).


Note that she will deposit only  4*18*$500 = $36,000.  The rest is what the account earns/accumulates in 18 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.