SOLUTION: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent

Question 1205192: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)
$200 is deposited monthly for 10 years at 3% per year in an account containing $7,000 at the start
FV = $
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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Find the amount accumulated FV in the given annuity account.
(Assume end-of-period deposits and compounding at the same intervals as deposits.
Round your answer to the nearest cent.)
$200 is deposited monthly for 10 years at 3% per year in an account containing $7,000 at the start
~~~~~~~~~~~~~~~~~~~~~~~

It works as if you have two separate accounts:


    (a) one account is the principal $7000 deposited once for 10 years at 3% per year compounded monthly;


    (b) and the other, which is an Ordinary Annuity plan with $200 deposits at the end of each month 
        at 3% per year compounded monthly.



For the first account, the future value after 10 years is

        FV1 =  = 9445.47  dollars  (rounded).



For the second account, the future value after 10 years is

        FV2 =  = 27948.28  dollars  (rounded).



Now, the future value of the original account in 10 years is the sum of these two amounts 


        FV = FV1 + FV2 = 9445.47 + 27948.28  = 37393.76 dollars.   


ANSWER.  Future value in 10 years is 37393.76 dollars.

Solved.

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To see other similar solved problems at this site, look into the lesson
- Ordinary annuity account with non-zero initial deposit as a combined total of two accounts
at this site.

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