Question

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.)

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)