Problem

$1$

: Finance in Perpetuity

You are offered one of the following two options for free. Option A includes a fixed cash flow of

$

$4$

$0$

$0$

$$every year forever that starts right now

$($

t

$=$

$0$

$)$

$$with the first payment at the end of this year

$($

t

$=$

$1$

$)$

$.$

$$Option B includes a fixed cash flow of $

$4$

$2$

$0$

$$every year forever, but it starts a year later

$($

t

$=$

$1$

$)$

$$with the first payment at the end of the next year

$($

t

$=$

$2$

$)$

$.$

$$Interest rates are at

$1$

$0$

$\%$

$$per

year for every maturity.

$1$

$.$

$$What is the value of Option A when it starts

$($

at t

$=$

$0$

$)$

$?$

$2$

$.$

$$What is the value of Option B when it starts

$($

at t

$=$

$1$

$)$

$?$

$3$

$.$

$$Which one should you pick and why?

Problem

$2$

: Student Loan Considerations

You graduate from LSU after four years with incredible memories and all the necessary skills for

a successful career in Business. However, you also carry about $

$6$

$0$

$,$

$0$

$0$

$0$

$$in student loans that you

need to plan for. Assume that the interest rate is fixed at

$8$

$\%$

$$per year with monthly compounding.

$1$

$.$

$$How much should you pay every month to fully repay your student loans in

$1$

$0$

$$years

$($

with

monthly compounding

$)$

$?$

$2$

$.$

$$How much should you pay every month to fully repay your student loans in

$2$

$0$

$$years

$($

with

monthly compounding

$)$

$?$

$3$

$.$

$$You get a $

$3$

$0$

$,$

$0$

$0$

$0$

$$signing bonus from your first job. Suppose that instead of buying a fancy

car, you decide to use the money to partially repay your loans. In that case, how much should

you pay every month to fully repay the remainder of your student loans in

$1$

$0$

$$years$?$

$($

with

monthly compounding

$)$

Problem

$3$

: Back from the Future

Time

$-$

travel will be invented in a few decades and your future

$-$

self pays you a visit to give you some

advice. You meet outside Starbucks, just as you are about to order your favorite venti white mocha,

quad shot

$($

$2$

$$shots on bottom,

$2$

$$on top

$)$

$,$

$$almond milk, extra hot, caramel drizzle

$($

inside the cup

$)$

with extra whip cream for $

$8$

$.$

$0$

$5$

$.$

$1$

$.$

$$Your future

$-$

self begs you not to order the drink, arguing that you can invest the amount in

the S&P

$5$

$0$

$0$

$$instead with an annual return of

$8$

$\%$

$$for the next

$4$

$0$

$$years$.$ If you do so

$,$

$$how

much money will you have in

$4$

$0$

$$years for every coffee you skip?

$2$

$.$

$$You skip the coffee for today! Also, your future

$-$

self informs you that you will attend two LSU

home football game every year, each of which will cost you about $

$2$

$,$

$0$

$0$

$0$

$$and encourages you

to limit your trips to one per year. How much money would you have in

$4$

$0$

$$years if you attend

only one game per year and invest the savings in the S&P

$5$

$0$

$0$

$$with an annual return of

$8$

$\%$

$?$

Problem

$4$

: Planning for Life

Right after graduating from LSU, you get your dream

$-$

job with a starting salary $

$1$

$0$

$0$

$,$

$0$

$0$

$0$

$$annually

$($

paid at the end of each year

$)$

$,$

$$which is expected to grow by

$5$

$\%$

$$every year. You plan to stay in

that job for

$3$

$0$

$$years and then retire. Your annual contribution to a

$4$

$0$

$1$

K os

$1$

$5$

$\%$

$$of your annual

salary

$($

including your employer

$$

s contributions

$)$

$.$

$$Your

$4$

$0$

$1$

K is expected to make an annual return

of

$1$

$1$

$\%$

$$until you retire. Assume annual payments and annual compounding.

$1$

$.$

$$Estimate your final annual salary before retirement.

$2$

$.$

$$Estimate how much money you would have in your

$4$

$0$

$1$

K by the time your retire

$($

t

$=$

$3$

$0$

$)$

$.$

$3$

$.$

$$At retirement, you decide to draw an annuity for the next

$2$

$5$

$$years by placing your funds in

an account that earns a guaranteed

$5$

$\%$

$$per year. Estimate your annual pension