Question

Luis has $170,000 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 20 years from now. If the new account earns interest at the rate of 2.5%/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 1

Luis has $170,000 in his retirement account (using the compound interest formula)

his current account (CA) after 20 years at 2.5% compounded quarterly is:

CA = 170000(1 + (0.025/4))^(4*20)

CA = 279846.82981

Luis also plans to put $3000/quarter into the new account until his retirement 20 yrs from now (using the annuity formula) The future value (FV) of the account is:

FV = 3000[(1 + (0.025/4))^(4*20) -1] / (0.025/4)

FV = 310155.75476

Total Amount = CA + FV

Total Amount = 279846.82981 + 310155.75476

Total Amount = 590002.58457

Luis will have $590002.58457 in his account at the time of his retirement.