You have decided to put $$500$ in the bank. The bank has given you $2$ options: $($A$)20$ percent interest compounded annually for $5$ years; or $($B$)8$ percent compounded quarterly for only $2$ years. Are these results surprising? Why or why not? $4.$ If you invest $$15,000$ today, how much will you have in $($HINT: You must use either MS Excel or the formulas$)$:A$.10$ years at $9\%$B$.12$ years at $13\%$C$.14$ years at $16\%$D$.19$ years at $19\%5.$ Southern & Company is considering the purchase of a new machine. If the machine will provide $$25,000$ annual savings for $10$ years and can be sold for $$50,000$ at the end of the period, what is the present value of the machine investment at an $8\%$ interest rate with savings realized at year end? $6.$ Answer the following questions.A$.$ You have decided to give your grandchild a graduation gift of $$10,000.$ The child will graduate in $18$ years. How much must you invest today if the bank guarantees you $3\%$ annual return?B$.$ Using the same example from $6$A$,$ your other option is to invest in a mutual fund. The $25-$year average return for the chosen mutual fund is $7\%.$ How much must you invest for the same return $($assuming no risk$)?7.$ For the following project, identify Net Present Value $($assuming an $8\%$ cost of capital$)$ and no salvage value after year $5.$ Then explain why you would accept or decline the project. Anticipated Cash Flows:Year $0($$$250,000)$Year $1$ $$90,000$Year $2$ $$110,000$Year $3$ $$40,000$Year $4$ $$30,000$Year $5$ $$40,0008.$ For the following project, identify Net Present Value $($assuming an $5\%$ cost of capital$)$ and no salvage value after year $5.$ Then explain why you would accept or decline the project. Anticipated Cash FlowsYear $0($$$40,000)$Year $1$ $$15,000$Year $2$ $$10,000$Year $3$ $$7,000$Year $4$ $$5,000$Year $5$ $$5,0009.$ In #$8$ above, describe a situation in which you would recommend the organization make the investment. $10.$ Nazarene Printing Company is considering the purchase of a new machine that will cost $$300,000$ and provide the following cash flows over the next five years: $$90,000,$ $$95,000,$ $$89,000,$ $$72,000,$ and $$65,000.$ Calculate the IRR for this piece of equipment. For further instructions on internal rate of return in Excel, see Appendix C$.11.$ Using the calculated IRR from #$10,$ do you make the investment if your:A$.$ Cost of capital is $4\%?$B$.$ Cost of capital is $10\%?$C$.$ Cost of capital is $13\%?12.$ Now, you are going to learn a shortcut for calculating IRR using the Present Value of an Ordinary Annuity Table in Appendix B$.$ For this shortcut, you begin by calculating the payback period for the capital investment. Then, find the number within the table that is closest to the payback period, and simply look at the percent column in which that number is located. Example: $$350,000$ investment with cash flows of $$100,000,$ $$90,000,$ $$75,000,$ $$60,000,$ and $$55,000.$ The MS Excel calculated IRR is $3\%.$ The payback period is $4\mathrm{.}5454.$ Within the table, the closest value we see is $4\mathrm{.}580$ under $3\%.$A$.$ Now your turn: $$500,000$ investment with cash flows of $$245,000,$ $$210,000,$ $$145,000,$ and $$57,000.$B$.$ Now try this: $$250,000$ investment with cash flows of $$96,000,$ $$74,000,$ $$45,000,$ $$31,000,$ $$13000,$ and $$23,000.13.$ You win the lottery and can either receive $$1,000,000$ as a lump sum or $$100,000$ per year for $20$ years. Assuming you can earn $8\%$ interest, which do you recommend and why? $14.$ BONUS: In your research, you have determined that to retire comfortably at age $70$ you must have at least $$1\mathrm{.}25$ million. You are now just graduating from college at age $22$ and wish to start saving for retirement right away. Your plan is to invest monthly and are conservatively assuming a $5\%$ annual return. How much must you invest each month to achieve your goal? Here is the formula you need to use. Solve for PMT$.$ A is the account balance after t years.PMT is the regular deposit amount.r is the annual rate of interest $($in decimal$)$n is the number of compounds per yeart is the number of years