[4 points] As the Head of Research & Development for a young start-up organization, you are always trying to manage large capital investments to maintain a sufficient amount of liquid (i.e. easily spendable) cash. Your team has recommended the purchase of a new machine that will cost $98,000 to purchase. This price has been guaranteed by the vendor for the next 8 years (i.e. the machine will cost $98,000 to purchase regardless of which year between now and the start of year 8 in which the machine is purchased). After this time, the price will increase to $128,000 which will be honored for any year of purchase starting in year 9. All purchases will be made at the end of the year and all deposits will be made at the start of the year. a. [2 points] If your company was to place $3800 into a savings account at the end of year 1 and every year thereafter until the purchase is made, and that account earns 7.33% interest per year, in what year (remember purchases are made at the end of the year only!) will you be able to purchase the machine? How much will the machine cost at the time of purchase? b. [2 points] Assume that your company will need to purchase the machine by the end of the year 7. How much would you need to deposit today, and at the end of each year (years 1 through 7) in order to have enough money saved for the purchase? Once again, assume that all deposits are equal in size and that they are made into the same account that earns 7.33% interest per year