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 dont 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?