Question

In: Finance

2. Mrs. D who 27 years old plans to retire at the age of 55. Mrs....

2. Mrs. D who 27 years old plans to retire at the age of 55. Mrs. D would like to be able to withdraw $132,000 per year from her retirement account for 45 years after retirement beginning the year after her retirement. She is also expecting an inheritance of $54,000 to be transferred to her on her 35th birthday. a How much does she need to have in her retirement account by retirement date if the interest rate is 6% per year during the post-retirement years? b Suppose she already has $12,000 in her retirement investment account that earns 9% per year. What will be the value of this amount by her retirement date? c Given her goal, her expected inheritance, and the investment she already has in 1b, how much does she need to invest per year from now till retirement (at 9% annual rate of return) in order to reach her retirement goal?

Expert Solution

Answer (a):

Retirement duration = 45 years

Annual withdrawal at the beginning of year = $132,000

Interest rate = 6%

Amount required in retirement account by retirement date = PV (rate, nper, pmt, fv, type) = PV (6%, 45, -132000, 0, 1)

= $2,162,580.027

Amount required in retirement account by retirement date = $2,162,580.03

Answer (b):

She already has $12,000 in her retirement investment account that earns 9% per year.

Current age = 27

Retirement age = 55

Years in investment = 55 - 27 = 28

Value of this amount by her retirement date = 12000 * (1 + 9%) ^28 = $134,005.674

Value of this amount by her retirement date = $134,005.67

Answer (c):

She is expecting an inheritance of $54,000 to be transferred to her on her 35th birthday.

Years in investment = 55 - 35 = 20

Value of this amount by her retirement date = 54000 * (1 + 9%)^20 = $302,638.181

Remaining balance required (at retirement date) = 2162580.027 - 134005.674 - 302,638.181 = $1,725,936.17

Amount she need to invest per year from now till retirement = PMT (9%, 28, 0, -1725936.17, 0) = $15278.07

Amount she need to invest per year from now till retirement = $15,278.07

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