Response:
At the time of retirement, Luis will possess $ 1,153,675.657524 in his retirement account.
Reasoning:
Luis currently has $170,000 in his retirement fund
After compounding at 4.5% quarterly for 30 years, his account will grow to
Account balance = $ 170,000(1 + (0.045/4))^(4*30)
Account balance = $ 650,838.260724
Moreover, Luis intends to contribute $2000 each quarter into the new account for the next 30 years prior to retirement.
The future value (FV) of this account is calculated as
FV = 2000[(1 + (0.045/4))^(4*30) -1] / (0.045/4) 0.01125
FV = $ 502,837.3968
To determine Luis’s total balance at retirement, we calculate the following:
Total amount
= Account balance + FV
Total amount = $ 650,838.260724 + $ 502,837.3968
Total amount = $ 1,153,675.657524
Luis will have $ 1,153,675.657524 in his retirement account.