All dollar values are REAL unless otherwise specified.

$1)$ You have a child that is $6$ years old, and would like to start saving up for their college education. You would like to be able to pay $$24,000$ a year for four years of college starting $12$ years from now $($when the child turns $18).$ How much do you need to save annually over the $12$ years to meet your goal, if you can earn a real annual return of $3\mathrm{.}5\%$ on your college savings account?

$2)$ An investment costs $$2400$ up front, but won$$t start paying off until three years from now, at which time it will return $$310$ per year for a period of ten years. If your real hurdle rate is $7\%,$ does this investment make sense?

$3)$ After graduating from IU$,$ you are hired by a company that offers a $401($k$)$ retirement plan. You would like to save enough in this plan so that when you retire in $55$ years you have an account balance of $$2\mathrm{.}1$ million. You plan to make monthly contributions, and expect a real annual return of $6\%,$ compounded monthly. How much should you deposit each month to reach your goal?

$4)$ The company you work for is trying to decide between two projects. Project $1$ costs $$160,000$ up front, and has an expected life of $4$ years, over which it will return $$52,000$ each of the four years. Project $2$ would last for $20$ years, costs $$1\mathrm{.}5$ million up front, and returns $$170,000$ at the end of each of the $20$ years. Assuming a real discount rate of $6\%,$ which project has the higher equivalent annual net benefit?

$5)$ You are offered $$1600($in nominal dollars$)7$ years from now in exchange for a loan of $$600$ today. You expect inflation to run $2\%$ per year, and your real hurdle rate is $5\mathrm{.}5\%.$ Should you make the loan?

$6)$ You would like to have $$20,000($in real $$)$ in an account $8$ years from now. If the inflation rate is expected to be $3\%,$ and you expect a nominal return of $5\%$ on the account, how much would you need to put in today?

$7)$ You take out a loan for $$16,000$ to buy a car that has equal nominal monthly payments over the next seven years. The real annual rate of return on the loan is $3\%,$ and the inflation rate is $1\%.$ What will the monthly payments be$?$

$8)$ You have $$600$ to invest, and are choosing between two projects, both of which cost $$600$ up front and will yield six years of returns. The returns for the first investment will be $$150($in nominal $$)$ per year. The returns for the second will be $$120($in real $$)$ per year. If your real hurdle rate is $5\%$ and the expected inflation rate is $2\mathrm{.}5\%,$ which of these investments should you choose $($if any$)?$

$9)$ You are analyzing a proposed project to renovate a local public recreation center. The project will cost $$500,000$ up front. It is expected that the value of the benefit to the community will be $$35,000($in nominal $$)$ per year for $20$ years. You and your team are unsure what discount rate would best proxy for the county residents time preferences and are unsure what future inflation will be$.$ You have decided to test the sensitivity of the results to using the CBO$$s recommended discount rate $(2\%)$ and the OMB$$s recommended discount rate $(7\%).$ In addition, you$$ve decided that expected inflation should fall somewhere between $2\%$ and $5\%$ annually. Perform a best and worst case sensitivity analysis. Based on this analysis do you think the county should move forward with this project?