4.37 You are 35 ycars old, and decide to save 5,000 cach ycar (with the first de

Question

4.37 You are 35 ycars old, and decide to save 5,000 cach ycar (with the first deposit onc ycar from now, in an account paying 8% interest per year. You will make your last deposit 30 years from now when you retire at age 65. During retirement, you plan to withdraw funds from the account at the end of each year (so your first withdrawal is at age 66) What constant amount will you be able to withdraw each year if you want the funds to last until you are 90? S1. Paul's younger and smarter brother, Sam, has just turned 40. He is planning to retire in 25 years, and has only 100K in his pension fund. He assumes he will live the same 20 years past his retirement date as his brother. At the beginning of each year of his retirement he plans to withdrawal 75K from his pension fund. To fund his required pension, Sam plans to deposit D each year (beginning today). Sam expects to earn 5% (after-tax), 2 compounded annually, on his account. What is the minimum value for D? S2. You have just turned 30, and have finally decided to put money to put into your retirement plan. With respect to the retirement plan rules, each dollar invested in the plan earns 7% per year. You cannot make withdrawals until after your 65th birthday. With respect to the retirement plan estimates, you plan to live to 100 and work until you turn 65. You will need $100,000 per year starting at the end of the first year of retirement and ending on your 100th birthday. You have decided to contribute a fixed percentage 100p% of your annual salary each year. Your starting salary is $75,000 per year and it will grow 2% per year until you retire. Determine the minimum value for p to fund your retirement plan. Answer to the nearest 0.01%

Explanation / Answer

4.37: Amount of annuity = $5,000. N = 30 and r = 8%

FVA of $1 for 30 years and 8% (from FVA table) = 113.2832

Thus amount available at retirement = amount deposited each year*113.2832 = 5,000*113.2832 = $566,416.06

Now there are a total of (90-65) = 25 withdrawals.

Present value of these withdrawals = $566,416.06

Let each withdrawal be "x". Thus x*PVA (25,8%) = 566,416.06

From PVA table we see that PVA of $1 for 25 years and 8% = 10.6748

Thus x*10.67478 = 566,416.06

or x = 566,416.06/10.6748

= $53,061.05

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