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 $3000/quarter into the new account until his retirement 20 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.)

Question

Mathematics

Slade Wang

10 September, 03:18

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 $3000/quarter into the new account until his retirement 20 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.)

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Jaylin Hester · Answer 1

Note: there is not enough money to be "rolled over" from the old account.

It will be assumed that he "tops up" the monthly payments to maintain a contribution of $3000/quarter to the new account.

Quarterly amount, A = $3000

interest per quarter, i = 0.035/4

Number of quarters over 20 years, n = 20*4=80

Future value (value in 20 years)

=A ((1+i) ^n-1) / i

=3000 ((1+.035/4) ^60-1) / (.035/4)

=235406.74 (to the nearest cent)