Luis has $170,000 in his retirement account at his present company. Because he i
ID: 2884319 • Letter: L
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 5.5%/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.)
Explanation / Answer
Luis has $170,000 in his retirement account (using the compound interest formula)
his current account (CA) after 30 years at 5.5% compounded quarterly is ,
CA = 170,000(1 + (0.055/4))^(4*30)
CA = 875292.0575
Luis also plans to put $2000/quarter into the new account until his retirement 30 years from now.
Here we need to use the annuity formula.
The future value (FV) of the account is :-
FV = 2000[(1 + (0.055/4))^(4*30) -1] / (0.055/4)
FV = 603458.4449
CA + FV = Total amount
Total amount = 875292.0575 + 603458.4449
Total amount = 1,478,750.5024
Luis will have $ 1,478,750.50 in his account at the time of his retirement.
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