SOLUTION: Luis has $110,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new acco

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Question 1148922: Luis has $110,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new account. Luis also plans to put $2000/quarter into the new account until his retirement 25 years from now. If the new account earns interest at the rate of 3.5%/year compounded quarterly, how much will Luis have in his account at the time of his retirement? Hint: Use the compound interest formula and the annuity formula. (Round your answer to the nearest cent.)
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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It works as a combination of two separate accounts:


    - one account is fixed principal of $110000 earning 3.5% compounded quarterly during 25 years, and


    - the second account is a classic Ordinary Annuity plan with the regular quarterly deposits of $2000 
      compounded quarterly at 3.5% annual percent rate.



For the first account, the formula and the final asset are

    Future value F1 = 110000%2A%281%2B0.035%2F4%29%5E%2825%2A4%29 = $262873.89


For the second account, the formula and the final asset are

    Future value F2 = P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29 = 2000%2A%28%28%281%2B0.035%2F4%29%5E%284%2A25%29-1%29%2F%28%280.035%2F4%29%29%29 = $317660.04.


Now the answer is the sum  F1 + F2 = $262873.89 + $317660.04 = $580533.93.

Solved.