SOLUTION: Determine the amount of the ordinary annuity at the end of the given period. (Round your final answer to two decimal places.) $400 deposited quarterly at 6.4% for 8 years $

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Question 1131683: Determine the amount of the ordinary annuity at the end of the given period. (Round your final answer to two decimal places.)
$400 deposited quarterly at 6.4% for 8 years
$

Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
FV=400(1.016)^32/0.016, assuming compounded quarterly. FV=C(1+i)^nt minus 1/i, where i =interest rate divided by number of compoundings per year.
The 32 is the number of quarterly compoundings for 8 years.
$16546.90

Answer by ikleyn(52824) 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,    (1)


where  FV is the future value of the account;  P is your quarterly payment (deposit); 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 = 400;  r = 0.64/4;  n = 4*8 = 32.  So, according to the formula (1), you get at the end of the 20-th year


    FV = 400%2A%28%28%281%2B0.064%2F4%29%5E%284%2A8%29-1%29%2F%28%280.064%2F4%29%29%29 = 400%2A%28%281.016%5E32-1%29%2F0.016%29 = $16546.90.


Note that you deposit only  4*8*$400 = $12,800.  The rest is what the account earns/accumulates in 8 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.