4.Solve the following questions. (Show all desired calculations and computations) (2*8=16 Marks)

You want to have $5,000,000 when you retire in 10 years. You expect to earn 12% compounded monthly over the entire 10-year period. How much extra money per month must you deposit if you choose to fund using an ordinary annuity technique rather than an annuity due technique? You want to buy an ordinary annuity that will pay you $4,000 a year for the next 20 years. You expect annual interest rates will be 8 percent over that time period. The maximum price you would be willing to pay for the annuity is..? With continuous compounding at 10 percent for 30 years, the future value of an initial investment of $2,000 is.? You are considering borrowing $100,000 for 30 years at a compound annual interest rate of 9 percent. The loan agreement calls for 30 equal annual payments, to be paid at the end of each of the next 30 years. (Payments include both principal and interest.) What is the annual payment that will fully amortize the loan? You have just graduated and have decided to purchase a brand new sports car to enjoy your newfound freedom. Your local credit union will provide financing for 60 months at a 9 percent annual rate, compounded monthly. You will give 15 percent of the $26,000 purchase price in cash to the dealer. The credit union will be used to finance the remaining 85 percent of the purchase price with the first payment due 1 month from today. What will be your monthly payment? What is the present value of a $6,000 ordinary annuity that earns 8% annually for an infinite number of periods? Your late Uncle Verns will entitles you to receive $5,000 at the end of every other year for the next two decades. The first cash flow is two years from now. If the compound annual interest rate is 15%, find the equivalent annual annuity pattern for two years. A bank offers you a nine-month certificate of deposit (CD) at a 12 percent annual rate that would provide a 12.36 percent effective annual yield. For the nine-month CD, is interest being compounded daily, monthly, semi-annually or quarterly? Explain your answer with calculations