SOLUTION: Someone opens an investment account with an initial deposit of $ 900. They then set up monthly deposits of $ 130 to the account. If the account earns 4.5% interest compounded month

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Question 1169701: Someone opens an investment account with an initial deposit of $ 900. They then set up monthly deposits of $ 130 to the account. If the account earns 4.5% interest compounded monthly, how much money will they have in the account in 7 years?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Someone opens an investment account with an initial deposit of $ 900.
They then set up monthly deposits of $ 130 to the account.
If the account earns 4.5% interest compounded monthly, how much money
will they have in the account in 7 years?
~~~~~~~~~~~~~~~~~~~~~~~~~ 


It works as if you have two separate accounts:


    (a) one account is the principal $900 deposited once for 7 years at 4.5% compounded monthly;


    (b) and the other, which is an Ordinary Annuity plan with $130 deposits at the end of each month 
        at 4.5% compounded monthly.



For the first account, the future value in 7 years is

        FV1 = 900%2A%281%2B0.045%2F12%29%5E%287%2A12%29 = 1232.51  dollars  (rounded).



For the second account, the future value in 7 years is

        FV2 = 130%2A%28%28%281%2B0.045%2F12%29%5E%287%2A12%29-1%29%2F%28%280.045%2F12%29%29%29%29 = 12807.68  dollars  (rounded).



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


        FV = FV1 + FV2 = 1232.51 + 12807.68  = 14040.19 dollars.    ANSWER

Solved.