The due date is $\frac{2}{9}\frac{?}{202423}$:$59pm.$ You may collaborate with your classmates in preparing the solutions, but each student must hand in a separate assignment. If you do receive help or work with another student on the assignment, you must note this fact at the beginning of your solutions. Please remember to put your name and section number or time at the top of the first page. Assignments that are late but within $24$ hours of the deadline, will receive $\frac{1}{2}$ credit. After $24$ hours no assignments will be accepted!

$($Retirement Problem$)$ You plan to retire in $30$ years $(4$ points$).$

In $50$ years, you want to give your daughter a $$500,000$ gift.

You will receive an inheritance of $$200,000$ in $25$ years.

You think you will want $$50,000$ per year when you retire for $30$ years $($the first withdrawal will come one year after you retire$).$

You will begin saving an amount to meet your retirement goals one year from today.

Required:

If you think you can make $9$ percent on your investments, how much will you need to save each year for the next $30$ years to meet your retirement goals?

Consider zero coupon bonds with a face amount of $$1,000.$ Fill in the following table with the prices of bonds with the stated maturity $($in years$)$ at the stated annually compounded yield $($interest rate$).$ For example, in the top left corner put the price of a $1$year zero coupon bond with a yield of $3\%.(4$ points$)$

$\backslash$table$[[,$Maturity $($years$)],[,1,5,10],[3\%,,,],[5\%,,,],[7\%,,,]]$

Suppose a hedge fund earns $1\%$ per month every month. $(4$ points$)$

a$.$ What is the EAR on an investment in this fund?

b$.$ If you need $$1$ million dollars in $5$ years, how much do you have to invest in the fund today?

c$.$ If you invest $$1$ million today, how much money will you have in $5$ years?

d$.$ If you invest $$1,000$ every month for $24$ months, starting immediately $($i$.$e$.,$ first investment at time $0,$ last investment $23$ months from now$),$ how much will you have at the end of $2$ years?

e$.$ If you need $$1$ million dollars in $5$ years, and you are going to invest the same amount every month for $24$ months, starting immediately $($i$.$e$.,$ just like part $($d$)$ above$)$ how much do you have to invest?

f$.$ If you invest today, how long will it take to triple your money?

Which is a better investment, an account paying $($i$)5\mathrm{.}00\%,$ annual compounding, $($ii$)4\mathrm{.}95\%,$ quarterly compounding, $($iii$)4\mathrm{.}90\%,$ monthly compounding, $($iv$)4\mathrm{.}85\%,$ continuous compounding? $(4$ points$)$

The table below gives the price of a stock at the end of each of the last ten years $($assume no dividends$).(4$ points$)$

a$.$ What is the arithmetic average annual return on the stock?

b$.$ What is the geometric average annual return on the stock?

c$.$ What is the annual HPR on the stock?

d$.$ What is your best estimate of the stock return for the year $2009?$

$\backslash$table$[[1999,2000,2001,2002,2003,2004,2005,2006,2007,2008],[$$$100,$$$70,$$$70,$$$90,$$$100,$$$125,$$$130,$$$150,$$$130,$$$90$