A: Calculate the present value of $5,000 received 5 years from today if your investments pay: a. 6% compounded annually b. 8% compounded annually c. 10% compounded annually d. 10% compounded semi-annually What do your answers to these questions tell you about the relation between present values and interest rates and between present values and the number of compounding periods per year? B: Suppose that you grow money in an account for four years at a return rate of 10%. Then this future amount is later invested for another four years. If your money triples by the end of the eight years total, then (to one decimal) what rate of return did you earn over the latter four years? 100 FV4 FV8=300 0 4 8 C: A contract features a lump-sum future flow of $46,000 three years from today. If you can now purchase that flow for $42,201.84, then what annual implied return would you earn on this contract? D: What is the present value of the following uneven stream? 240 795 628 179 k= 11.5% 0 1 2 3 E: An annuity contract will make 8 annual payments and the first payment occurs exactly a year from today. If the annuity has a 9.2% rate and a current PV or price of $308.98, then what must be the size of its annual payments? F: An annuity makes monthly payments of $235 at the end of every month. If it has a term of 60 months and an annual interest rate of 6%, then what is its present value? Question G: For the mixed stream of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 12% assuming no withdrawals are made during the period and that the deposits are made: a. At the end of each year. b. At the beginning of each year. Year Cash Flows 1 30,000 2 25,000 3 20,000 4 10,000 5 5,000 H: Construct a Loan Amortization Schedule for a $6000, 10% interest rate loan that is re-paid semi-annually over 4 years. (Hint: First solve for the semi-annual payment, then construct the schedule) I (Bonus) You originally took out a $435,000, 360-month loan 8 years ago and have made 96 monthly payments of $3,161.60. You can now refinance that loan with a new 264-month loan that has an annual interest rate 5.86%. If you refinance the loan, then to the nearest dollar, how much money will you save each month on your monthly mortgage payment? Question 10: You have decided to endow your favorite university with a scholarship. It is expected to cost $6,000 per year to attend the university into perpetuity. You expect to give the university the endowment in 10 years and will accumulate it by making annual end of year deposits into an account. The rate of interest is expected to be 10% for all future time periods. a. How large must the endowment be? b. How much must you deposit at the end of each of the next 10 years to accumulate the required amount? c. If you want your $6,000 to grow by 3% every year to compensate for inflation, how will your answer differ in b? Question 11: Gina Vitale has just contracted to sell a small parcel of land that she inherited a few years ago. The buyer is willing to pay $24,000 at the closing of the transaction or will pay the amounts shown in the following table at the beginning of each of the next 5 years. Because Gina doesn't really need the money today, she plans to let it accumulate in an account that earns 7% annual interest. Given her desire to buy a house at the end of 5 years after closing on the sale of the lot, she decides to choose the payment alternative- $24,000 single amount or the mixed stream of payments in the following table -that provides the higher future value at the end of 5 years. Which alternative do you think she should choose? Why? Beginning of Cash Flow Year 1 2000 2 4000 3 6000 4 8000 5 10000

Question 1: Calculate the present value of $5,000 received 5 years from today if your investments pay: a. 6% compounded annually b. 8% compounded annually c. 10% compounded annually d. 10% compounded semi-annually What do your answers to these questions tell you about the relation between present values and interest rates and between present values and the number of compounding periods per year? Question 2: Suppose that you grow money in an account for four years at a return rate of 10%. Then this future amount is later invested for another four years. If your money triples by the end of the eight years total, then to one decimal) what rate of return did you earn over the latter four years? 100 FV4 FV=300 | 0 4 8 Question 3: A contract features a lump-sum future flow of $46,000 three years from today. If you can now purchase that flow for $42,201.84, then what annual implied return would you earn on this contract? Question 4: What is the present value of the following uneven stream? 240 795 628 179 H k= 11.5% 1 2 3 Question 5: An annuity contract will make 8 annual payments and the first payment occurs exactly a year from today. If the annuity has a 9.2% rate and a current PV or price of $308.98, then what must be the size of its annual payments? Question 6: An annuity makes monthly payments of $235 at the end of every month. If it has a term of 60 months and an annual interest rate of 6%, then what is its present value? For the mixed stream of cash flows shown in the following table, determine the future value at the end of the final year if deposits are made into an account paying annual interest of 12% assuming no withdrawals are made during the period and that the deposits are made: a. At the end of each year. b. At the beginning of each year. Year Cash Flows 1 30,000 2 25,000 3 20,000 4 10,000 5 5,000 Question 8: Construct a Loan Amortization Schedule for a $6000, 10% interest rate loan that is re-paid semi-annually over 4 years. (Hint: First solve for the semi-annual payment, then construct the schedule) Question 9 (Bonus) You originally took out a $435,000, 360-month loan 8 years ago and have made 96 monthly payments of $3,161.60. You can now refinance that loan with a new 264-month loan that has an annual interest rate 5.86%. If you refinance the loan, then to the nearest dollar, how much money will you save each month on your monthly mortgage payment