$1.$ You are offered an asset costing $$600$ that has cash flows of $$100$ at the end of each of the next $10$ years.

a$.$ If the appropriate discount rate for the asset is $8\%,$ should you purchase it$?$ b$.$ What is the IRR of the asset?

$2.$ You just took a $$10,000,5-$year loan. Payments at the end of each year are flat $($equal in every year$)$ at an interest rate of $15\%.$ Calculate the appropriate loan table, showing the breakdown in each year between principal and interest.

$3.$ You have just turned $35,$ and you intend to start saving for your retirement. Once you retire in $30$ years $($when you turn $65),$ you would like to have an income of $$100,000$ per year for the next $20$ years. Calculate how much you would have to save between now and age $65$ in order to finance your retirement income. Make the following assumptions:

$$ All savings draw compound interest of $10\%$ per year.

$$ You make the first payment today and the last payment on the day you turn $64(30$ payments$).$

$$ You make the first withdrawal when you turn $65$ and the last withdrawal when you turn $84(20$ payments$).$