Luis has $120,000 in his retirement account at his present company. Because he i

Question

Luis has $120,000 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 $3000/quarter into the new account until his retirement 25 years from now. If the new account earns interest at the rate of 5.5%/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.)

Explanation / Answer

Luis has $120,000 in his retirement account (using the compound interest formula)
his current account (CA) after 25 years at 5.5% compounded quarterly is:
CA = 120000(1 + (0.055/4))^(4*25)
CA = 470184.131

Luis also plans to put $3000/quarter into the new account until his retirement 25 yrs from now (using the annuity formula) The future value (FV) of the account is:
FV = 3000[(1 + (0.055/4))^(4*25) -1] / (0.055/4)
FV = 843285.069

CA + FV = Total
Total = 470184.131 + 843285.069
Total = 1313469.2

Luis will have $1,313,469.2  in his account at the time of his retirement

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