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 $2000/quarter into the new account until his retirement 30 years from now. If the new account earns interest at the rate of 4.5%/year compounded quarterly, how much will Luis have in his account at the time of his retirement

Answer 1

Luis will have approximately $894,004.79 in his retirement account at the time of his retirement.

Step-by-step explanation:

To calculate how much Luis will have in his retirement account at the time of his retirement, we need to consider the initial amount in his account and the additional contributions he plans to make. The initial amount is $170,000, and he plans to contribute $2000 quarterly for 30 years.

First, we need to calculate the future value of the initial amount after 30 years, using the formula for compound interest:

Future Value = Present Value × (1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods × Number of Years)

Using the given interest rate of 4.5% per year compounded quarterly, we can plug in the values into the formula:

Future Value = $170,000 * (1 + 0.045/4)^(4 × 30)

After calculating this, we find that Luis will have approximately $894,004.79 in his retirement account at the time of his retirement.

Answer 2

Luis will have $ 1,153,675.657524 in his account at the time of his retirement.

Step-by-step explanation:

Acording to the data Luis has $170,000 in his retirement account

His current account after 30 years at 4.5% compounded quarterly will be

Current account = $ 170,000(1 + (0.045/4))^(4*30)

Current account = $ 650,838.260724

Acording to the data Luis also plans to put $2000/quarter into the new account until his retirement 30 years from now.

The future value (FV) of the account will be

FV = 2000[(1 + (0.045/4))^(4*30) -1] / (0.045/4) 0.01125

FV = $ 502,837.3968

Therefore, to calculate how much will Luis have in his account at the time of his retirement we have to calculate the following:

Total amount = Current account+FV

Total amount = $ 650,838.260724 + $ 502,837.3968

Total amount = $ 1,153,675.657524

Luis will have $ 1,153,675.657524 in his account at the time of his retirement.