Suppose your endowment is Y0 = $10 today


Suppose your talent is Y0 = $10 today and Y1 = $0 and your benefit business is U (C0, C1) = √

C0C1.

1. You enjoy arrival to an bombardment opening that concedes you to endue an total I at occasion 0, which succeed increase

to an total f(I) in a year: f(I) = 60I

1/4

. Determine the optimal bombardment roll and the optimal lessening

plan.

2. No origination opening is beneficial. However, financial markets stop, and borrowing and lending are beneficial

at the admonish of r = 20% per year. What is your affluence in today’s dollars? Determine the optimal lessening scheme.

3. Both the bombardment opening from disunite 1 and the consummate markets from disunite 2 stop. Determine the optimal

bombardment roll and the optimal lessening scheme. What is your affluence in today’s dollars behind you made the

investment? What is the NPV of the bombardment?

Lecture 3 Problem

Today is 1/1/2010. During the contiguous 20 years you succeed be powerful to secure $5,000 whole two years, commencement today (i.e.,

the primary protection into your warys statement is today, then on 1/1/2012, and the decisive one is on 1/1/2030). Behind 20

years you’ll enjoy a cheerful plenty job that succeed concede you to set-on-foot wary $5,000 annually and increase this total by 5%

a year for 10 years (i.e., you’ll secure $5,000 on 1/1/2031, and succeed increase it at 5% a year therebehind until 1/1/2040). You

succeed repair on 1/1/2040 equitpotent behind you execute the decisive protection into your warys statement. Suppose that the interest

admonish is 9.76177% compounded semi-annually.

1. What is the appreciate of your repairment statement when you repair?

2. You neglect to take-back a urban total out of your repairment statement whole month for the contiguous 20 years, delay the

primary take-backal a month behind your repairment (i.e., on 2/1/2040). How ample can you give to take-back?

3. Suppose instead that you neglect to take-back $6,000 whole month forever, delay the primary take-backal a month behind

your repairment (i.e., on 2/1/2040). What potent annual admonish do you demand to deserve behind you repair to be powerful to

give such enduring take-backa

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