Question

Ruby is 25 and has a good job at a biotechnology company. She currently has $10,000 in an IRA, an important part of her retirement nest egg. She believes her IRA will grow at an annual rate of 8 percent, and she plans to leave it untouched until she retires at age 65. Ruby estimates that she will need $875,000 in her total retirement nest egg by the time she is 65 in order to have retirement income of $20,000 a year (she expects that Social Security will pay her an additional $15,000 a year). a. How much will Ruby’s IRA be worth when she needs to start withdrawing money from it when she retires? Use Exhibit 1-A. (Round FV factor to 3 decimal places and final answer to the nearest whole dollar.) b. How much money will she have to accumulate in her company’s 401(k) plan over the next 40 years in order to reach her retirement income goal? (Round your answer to the nearest whole dollar.)

Answer 1

Answer:

a. How much will Ruby’s IRA be worth when she needs to start withdrawing money from it when she retires?

the future value of Ruby's IRA = $10,000 x 21.725 (FV factor, 8%, 40 periods) = $217,250

b. How much money will she have to accumulate in her company’s 401(k) plan over the next 40 years in order to reach her retirement income goal?

she needs to accumulate $875,000 - $217,250 = $657,750 during the next 40 years

the annual contribution = FV / FV annuity factor = $657,750 / 259.057 (FV annuity factor, 8%, 40 periods) = $2,539.02 per year