# Optimal Investment Assignment | Homework For You

Suppose your endowment is Y0 = \$10 today and Y1 = \$0 and your utility function is U (C0, C1) = √

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C0C1.

1. You have access to an investment opportunity that allows you to invest an amount I at time 0, which will grow to an amount f(I) in a year: f(I) = 60I

1/4

. Determine the optimal investment level and the optimal consumption plan.

2. No production opportunity is available. However, financial markets exist, and borrowing and lending are available at the rate of r = 20% per year. What is your wealth in today’s dollars? Determine the optimal consumption plan.

3. Both the investment opportunity from part 1 and the capital markets from part 2 exist. Determine the optimal investment level and the optimal consumption plan. What is your wealth in today’s dollars after you made the investment? What is the NPV of the investment?

Lecture 3 Problem

Today is 1/1/2010. During the next 20 years you will be able to save \$5,000 every two years, beginning today (i.e., the first deposit into your savings account is today, then on 1/1/2012, and the last one is on 1/1/2030). After 20 years you’ll have a good enough job that will allow you to start saving \$5,000 annually and grow this amount by 5% a year for 10 years (i.e., you’ll save \$5,000 on 1/1/2031, and will grow it at 5% a year thereafter until 1/1/2040). You will retire on 1/1/2040 right after you make the last deposit into your savings account. Suppose that the interest rate is 9.76177% compounded semi-annually.

1. What is the value of your retirement account when you retire?

2. You want to withdraw a fixed amount out of your retirement account every month for the next 20 years, with the first withdrawal a month after your retirement (i.e., on 2/1/2040). How much can you afford to withdraw?

3. Suppose instead that you want to withdraw \$6,000 every month forever, with the first withdrawal a month after your retirement (i.e., on 2/1/2040). What effective annual rate do you need to earn after you retire to be able to afford such perpetual withdrawal. Get Finance homework help today

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