Since you are a responsible professional, you are starting to invest and plan for retirement early. You are committing y

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Since you are a responsible professional, you are
starting to invest and plan for retirement early. You are
committing yourself to make annual contributions of $20,000 to your
investment account and you start at the age of 25. Since you have a
long-term investment horizon, you are investing your retirement
funds into a broadly-diversified equity index fund where you can
expect to earn an 8% return p.a. Once you are retired, your
funds will remain invested but in a more conservative portfolio
where you can expect a 5% return. For planning purposes, you assume
that you live until the age of 90 and you don’t plan to leave an
inheritance behind at the end of your lifespan (you take care of
your descendants with a life insurance you have purchase outside of
your retirement investment account).
Answer the following questions and please clearly
indicate which answers relate to which question. Please type down
your step by step calculation to get partial credits. If you use
formulas or excel functions, please indicate which formulas or
functions you are using and what are your
inputs.
1. If you save for 40 years and
retire at the age of 65, to what amount has your investment account
grown to? Given your expected remaining lifespan of 25 years, how
much can you withdraw annually from your retirement
account?
2. After looking at all those
numbers you decide to commit yourself to a frugal lifestyle during
your retirement years, but in return you want to retire at the age
of 50. If you want to withdraw $150,000 per year during your
retirement from age 50 to 90, what is the amount you have to
contribute to your investment account each year during your savings
years from age 25 to age 50?