SOLUTION: Jane Adele deposits $1,300 in an account at the beginning of each 3-month period for 12 years. If the account pays interest at the rate of 4%, compounded quarterly, how much will s

Question 1198679: Jane Adele deposits $1,300 in an account at the beginning of each 3-month period for 12 years. If the account pays interest at the rate of 4%, compounded quarterly, how much will she have in her account after 12 years?

Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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Jane Adele deposits $1,300 in an account at the beginning of each 3-month period for 12 years.
If the account pays interest at the rate of 4%, compounded quarterly,
how much will she have in her account after 12 years?
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It is a classic Annuity Due saving plan. The general formula is 


    FV = ,    (1)


where  FV is the future value of the account;  P is the quarterly payment (deposit) 
at the beginning of each payment period; r is the quarterly 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 = 1300;  r = 0.04/4 = 0.01;  n = 12*4 = 48.  
So, according to the formula (1), Jane Adele will get at the end of the 4-th year


    FV =  =   = $80385.28  (rounded).


Note that Jane Adele will deposit only  12*4*$1300 = $62400 in 12 years.  
The rest is what the account earns/accumulates in 12 years.

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On Annuity Due saving plans, see the lesson
- Annuity Due saving plans and geometric progressions
in this site.

This lesson contains EVERYTHING you need to know about this subject, in clear and compact form.

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