SOLUTION: Hi there, I’ve been stuck on this question for a day now and I’ve been using the reccurance relation formula to find out the answer but I’m struggling to get the correct on

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Question 1144002: Hi there,
I’ve been stuck on this question for a day now and I’ve been using the reccurance relation formula to find out the answer but I’m struggling to get the correct one. I’m not even sure if I’m meant to use that formula...
Josie makes an initial deposit of $5000 on an investment taken out over 10 years at a rate of 7.4% per annum compounding biannually and an additional deposit of $500 is made every six months. How much interest has been earned over this time?
Thank you (:
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.

            For me, the original text is some soup prepared using English words  (or something recalling English words),
            but without a clear plan,  without an exact prescription and without knowledge of relevant terminology.

            Where did you take it ?   From your phone ?   Certainly,  not from a textbook.

            This soup is not a Math problem.  To get a status of a Math problem,  it must be edited and totally re-written.

            My editing is THIS : 

              Josie opened an account by depositing $5000 at the very beginning and then adding $500 regularly 
              at the end of every six months. The account is for 10 years and has the rate of 4.7% per annum 
              compounded semiannually. How much interest the account earns over this time?


            If you agree with my editing, then find my solution below.

            If you do not agree,  then please let me know  WHY.


Solution 

This account works as two separate saving plans:

    - one plan is the initial deposit of $5000 for 10 years at the rate of 4.7% per annum compounded semi-annually,  and

    - the other plan is an Ordinary Annuity for 10 years with regular deposits of $500 every six months at the rate 
      of 4.7% per annum compounded semi-annually


First account works according to the formula

    FV%5B1%5D = 5000%2A%281%2B0.047%2F2%29%5E%282%2A10%29


Second account is Ordinary Annuity saving plan and works according the formula

    FV%5B2%5D = 500%2A%28%28%281%2B0.047%2F2%29%5E%282%2A10%29-1%29%2F%28%280.047%2F2%29%29%29.


Calculate future value  FV%5B1%5D  and  future value  FV%5B2%5D, then add them and subtract (5000 + 2*500*10) = 15000 dollars 
that Josie deposited from the very beginning to the end in 10 years.


Then the expression  FV%5B1%5D + FV%5B2%5D - 15000  dollars will be your answer.

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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.