Question

Luis has $120,000 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 30 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

Solution:

First,we have to calulate the future value of $120,000 using interest rate of 3.5 per year compounded quarterly

Future value=$120,000*(1+0.035/4)^30*4

=$120,000*2.84463

=$341,355.55

Now,we have to calculate the future value of contious payment(annuity) of $3000

Future value=$3000*[(1+0.035/4)^30*4/(0.035/4)]

=$3000*210.814813

=$632,444.44

Thus,the amount Luis will have in his account at the time of his retirement is;

=$341,355.55+$632,444.44

=$973,799.99