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ASSIGNMENTNUMERICALS OF TIME VALUE OF MONEYIf you deposit $10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years?What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.Your parents are planning to retire in 18 years. They currently have $250,000, and they would like to have $1,000,000 when they retire. What annual rate of interest would they have to earn on their $250,000 in order to reach their goal, assuming they save no more money?What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.Your broker offers to sell you a note for $13,250 that will pay $2,345.05 per year for 10 years. If you buy the note, what interest rate (to the closest percent) will you be earning?A mortgage company offers to lend you $85,000; the loan calls for payments of $8,273.59 per year for 30 years. What interest rate is the mortgage company charging you?What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent? If interest rates in general were to double and the appropriate discount rate rose to 14 percent, what would happen to the present value of the perpetuity?The prize in last week’s Florida lottery was estimated to be worth $35 million. If you were lucky enough to win, the state will pay you $1.75 million per year over the next 20 years. Assume that the first installment is received immediately. a. If interest rates are 8 percent, what is the present value of the prize?b. If interest rates are 8 percent, what is the future value after 20 years?c. How would your answers change if the payments were received at the end of each year?Your client is 40 years old and wants to begin saving for retirement. You advise the client to put $5,000 a year into the stock market. You estimate that the market’s return will be, on average, 12 percent a year. Assume the investment will be made at the end of the year.a. If the client follows your advice, how much money will she have by age 65?b. How much will she have by age 70?Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1; that is, they are ordinary annuities. Assume that compounding occurs once a year.a. $400 per year for 10 years at 10 percent.b. $200 per year for 5 years at 5 percent.c. $400 per year for 5 years at 0 percent.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.Find the present value of the following ordinary annuities. Assume that discounting occurs once a year.a. $400 per year for 10 years at 10 percent.b. $200 per year for 5 years at 5 percent.c. $400 per year for 5 years at 0 percent.d. Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities pute the future value of $1,000 compounded annually fora. 10 years at 5 percent.b. 10 years at 7 percent.c. 20 years at 5 percent.d. Why is the interest earned in part c not twice the amount earned in part a?Calculate the present value of the following cash flows discounted at 10 percent.a. $1,000 received seven years from today.b. $2,000 received one year from today.c. $500 received eight years from today.4.3 Would you rather receive $1,000 today or $2,000 in 10 years if the discount rate is 8 percent?The government has issued a bond that will pay $1,000 in 25 years. The bond will payno interim coupon payments. What is the present value of the bond if the discount rateis 10 percent?A firm has an estimated pension liability of $1.5 million due 27 years from today. If thefirm can invest in a risk-free security that has a stated annual interest rate of 8 percent, how much must the firm invest today to be able to make the $1.5 million payment?You have won the Florida state lottery. Lottery officials offer you the choice of thefollowing alternative payouts:Alternative 1: $10,000 one year from now.Alternative 2: $20,000 five years from now.Which alternative should you choose if the discount rate is:a. 0 percent?b. 10 percent?c. 20 percent?d. What discount rate makes the two alternatives equally attractive to you?You are selling your house. The Smiths have offered you $115,000. They will pay youimmediately. The Joneses have offered you $150,000, but they cannot pay you until threeyears from today. The interest rate is 10 percent. Which offer should you choose?Suppose you bought a bond that will pay $1,000 in 20 years. No intermediate couponpayments will be made. If the appropriate discount rate for the bond is 8 percent,a. what is the current price of the bond?b. what will the price be 10 years from today?c. what will the price be 15 years from today?What is the future value three years hence of $1,000 invested in an account with a statedannual interest rate of 8 percent,a. compounded annually?b. compounded semiannually?c. compounded monthly?d. compounded continuously?e. Why does the future value increase as the compounding period shortens?Calculate the present value of $5,000 in 12 years at a stated annual interest rate of 10percent, compounded quarterly.Bank America offers a stated annual interest rate of 4.1 percent, compounded quarterly,while Bank USA offers a stated annual interest rate of 4.05 percent, compounded monthly. In which bank should you deposit your money?The market interest rate is 15 percent. What is the price of a consol bond that pays$120 annually?A prestigious investment bank designed a new security that pays a quarterly dividend of$10 permanently. What is the price of the security if the stated annual interest rate is 12percent, compounded quarterly?World Transportation, Inc., is expected to initiate its quarterly dividend of $1 five yearsfrom today and the dividend is expected to remain constant permanently. What is the price of World Transportation stock if the stated annual interest rate is 15 percent, compounded quarterly?Should you buy an asset that will generate income of $1,200 per year for eight years? Theprice of the asset is $6,200 and the annual interest rate is 10 percent.What is the value of a 15-year annuity that pays $500 a year? The annuity’s first payment is at the end of year 6 and the annual interest rate is 12 percent for years 1 through 5 and 15 percent thereafter. ................
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