PS# 6 Time Value of Money FM: Chapter 4 # 9, 12, 13, 24, 29 & 33

(4-9) Find the following values, using the equations, and then work the problems using a financial Present and Future Values of Single Cash Flows for Different Periods calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) a. An initial $500 compounded for 1 year at 6% b. An initial $500 compounded for 2 years at 6% c. The present value of $500 due in 1 year at a discount rate of 6% d. The present value of $500 due in 2 years at a discount rate of 6% (429) Loan Amortization Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%; it calls for payments every 6 months, beginning on June 30 , and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during theyear. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year (4-33) Required Annuity Payments Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires-that is, until age 85 . He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has $100,000 saved and expects to earn a return on his savings of 8% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) You want to accumulate $1 million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (ile., your second deposit will be 3% greater than your first the third wil. be 3% greater than the second, etc.). How much must your first deposit be if you are to meet your goal? (4-12) Future Value of an Annuity Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. (Notes: See the Hint to Problem 4-9. Also note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.) a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due. (4-24) To complete your last year in business school and then go through law school, you will Payment need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 7% interest, a sum of money that is sufficient to provide the four payments of $10,000 each. His deposit will be made today. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal? After the last withdrawal? (4-13) Find the present value of the following ordinary annuities (see the Notes to Problem 4-12). Present Value of an Annuity a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0% d. Now rework parts a, b, and c assuming that payments are made at the beginning o each year; that is, they are annuities due