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applications of the time value of money

Questions and Answers of Applications Of The Time Value Of Money

. Let A and B be jointly uniformly distributed over the quarter-circle A^ A- < 1, /4 > 0, 5 > 0. Show that the probability that the equation- (B - l ) - 0 has no real roots is p = 2/n.
. A carnival game consists of throwing a coin onto a table top marked with contiguous squares of sidea. If the coin does not touch any line the player wins. If the coin has radius r, show that the
. Two numbers, X and E, are chosen independently and uniformly on (0,1 ).Show that the probability that their sum is greater than one while the sum of their squares is less than one is p = 7t/4 - 1
. Two points P, and ? 2 are chosen independently and uniformly on (0,1).What is the probability that the distance between P , and P2 is less than the distance from 0 to Pi? (Ans: 3/4).
. If X is uniformly distributed on (0, 1 ) and Y is uniformly distributed on(0 , 2 ), find the probabilities that(i) x + r > 1(ii) y 1.Assume X and Y are independent. (Ans: 3/4; 2/3).
. A point P = (X, Y) is chosen randomly on the unit square. Calculate the probability that P is closer to (0,0) than it is to (¿,^). (Ans: 1/8).
Under what conditions does the effective annual rate of interest (EAR) differ from the annual percentage rate (APR)?
As the frequency of compounding increases within the annual period, what happens to the relation between the EAR and the APR?
If interest is paid at a rate of 5% per year, compounded quarterly, what is the:a. annual percentage rate?b. effective annual rate?
L. Shark is willing to lend you $10,000 for three months. At the end of six months, L. Shark requires you to repay the $10,000, plus 50%.a. What is the length of the compounding period?b. What is the
The Consistent Savings and Loan is designing a new account that pays interest quarterly. They wish to pay, effectively, 16% per year on this account. Consistent S & L wants to advertise the annual
If the annual percentage rate is 9.5% and interest compounds continuously, what is the effective annual rate of interest?
If the annual percentage rate is 10% and interest compounds quarterly, what is the effective annual rate of interest?
Consider an investment that earns 5% in the first year, 6% in the second year, and 7% in the third year. What is the time-weighted return on this investment?
Consider an investment that requires $5,000 today, but promises$4,000 one year from today and $2,000 two years from today. What is the money-weighted return on this investment?
If a mortgage requiring monthly payments is advertised as having a 6% APR, what is the effective annual rate on this mortgage?
What is the amount of periodic payment needed to repay a loan of$50,000 in 30 monthly payments if the APR on this loan is 6%?
Consider the terms for two loans for a loan of $100,000:Loan A. Paid back in 24 end-of-month payments of $4,707.35 each Loan B. Paid back in eight end-of-quarterly payments of $19,779.90 each Which
Complete the following table for a loan of $15,000 that is repaid with three annual payments of $6,000 each: Beginning Principal Ending Period Balance Payment Interest Repayment Balance 123 Today 1
Suppose a car dealership is advertising a car loan with a 3% APR, and monthly payments over three years.a. If you buy a car and finance $30,000 with this loan, what is the amount of your monthly
Consider a loan of $100,000 that requires four annual installments of $28,201 each. Amortize this loan using the following table: Period Beginning Balance Principal Ending Payment Interest Repayment
Suppose you borrow $10,000 and are required to pay this back in three annual installments. And suppose the interest rate on this loan is 10%. What is the required payment each year?
Suppose you borrow $2,000 today and expect to pay $150 at the end of each year. If the interest rate is 6%, how long will it take to pay off the $2,000 loan?
Suppose you borrow $150,000 and pay it back over 20 years in annual payments. If the interest rate is 5%, complete the following information corresponding to the second year’s payment: Loan Payment
The Car Company will lend you $10,000 for your new car purchase.The Car Company requires that you pay the loan back in monthly payments of $332.14 each, for 36 monthly payments. What is the annual
Suppose you can choose between two loans for $50,000, each with an APR of 6%: Loan 1 Loan 2 Term 36 months 36 months Balloon payment at the end of the loan $0 $10,000 What is the amount of monthly
If the discount rate is 5%, what is the present value of a series of four annual $5,000 cash flows, with the first cash flow occurring three periods from today?
If the discount rate is 5%, what is the present value of a series of 10 annual $5,000 cash flows, with the first cash flow occurring 20 periods from today?
If the discount rate is 5%, what is the present value of a series of four annual $5,000 cash flows, with the first cash flow occurring two years from today?
If you can earn 5% on your deposits, how much would you have to deposit in an account at the end of each year, starting at the end of this year, for 19 years, so that you can make 10 withdrawals of
Joe Investor is planning to retire in 20 years. He is guessing that he will live for 30 years past his retirement. He figures he needs $100,000 per year to live on, with his first withdrawal on his
Warren Wealthy wants to save for his retirement. His goal is to retire at 60 and have $60,000 per year to live on for 25 years, with the first withdrawal on his 61st birthday and the last withdrawal
Suppose you plan to retire on your 65th birthday and wish to begin withdrawing from your retirement savings beginning with your 66th birthday. And suppose that your savings earn 2% per year. If you
Suppose you plan to retire on your 65th birthday and wish to begin withdrawing from your retirement savings beginning with your 66th birthday, but have $10,000 left over when you die to cover your
An insurance salesperson is offering to sell you an annuity. The terms of the annuity are that you purchase this annuity today, on your 50th birthday; the annuity of $20,000 for 20 years begins on
Suppose you buy an insurance policy today for $2 every week, starting next week that provides $10,000 for final expenses (burial insurance).How many years must you live for this to be a wise decision
Complete the following table, indicating whether the bond will be selling for a premium or a discount from its face value: Bond Coupon Rate Yield to Maturity Premium or Discount? 5% ABCD 4% 6% 5% 4%
What is the value of a $1,000 face value bond that has five years remaining to maturity, a coupon rate of 8% (paid semiannually), and is priced to yield 10%?
What is the value of a $1,000 face value bond that has four years remaining to maturity, a coupon rate of 5% (paid semiannually), and is priced to yield 4%?
What is the current value of a five year, $1,000 face value bond that is priced to yield 6% and has a coupon rate of 10%?
ABC, Inc. has a bond outstanding with eight years remaining to maturity and a coupon rate of 8% paid semiannually. If the current market quote is 88, what is the yield to maturity (YTM) on the ABC
The DEF Company bonds have a face value of $1,000 and mature in five years. The bonds pay 4% interest in the first two years and 6%thereafter. Interest is paid semiannually. If you buy a DEF bond
What is the current value of a $500 face value bond that is priced to yield 6%, has a coupon rate of 8%, and has four years remaining to maturity?
Suppose a $1,000 face value, zero-coupon bond has five years remaining to maturity. The bond is currently priced to yield 5%. What is the value of this bond?
Suppose a $1,000 face value, zero-coupon bond has five years remaining to maturity. The bond’s current quote is 70. What is the yield to maturity on this bond?
Which of the following two bonds has the higher yield to maturity?Bond 1. Five years remaining to maturity; coupon rate of 5%; the bond has a current quote of 94.Bond 2. Seven years remaining to
Suppose the ABC stock has a current dividend of $10.00 per share. If dividends grow at a rate of 3% per year, forever, and if the required rate of return on ABC stock is 12%, what is the value of a
The DEF Company stock pays a dividend of $1.50 per share. If the growth rate of future dividends is expected to be 5% per year, for the foreseeable future and if the required rate of return is 10%,
Investors expect the GHI Company to pay $2.50 in dividends next year and the growth rate of future dividends to be 1%. If the required rate of return is 12%, what is the current value of a share of
The XYZ Company currently pays a dividend of $2.00 per share.Dividends are expected to decline at a rate of 5% per year for the foreseeable future. If the required rate of return is 12%, what is the
A stock currently pays a dividend of $2 for the year. Expected dividend growth is 20% for the next three years and 7% thereafter for an indefinite amount of time. The appropriate required rate of
Suppose you buy a stock for $20 per share at the end of 2009. If you receive $3 of dividends at the end of 2010 and sell the stock for $25 at the end of 2011, what is your return on this stock?
Intermark, Inc. paid dividends of $0.055 per share in 2007. In 2011, Intermark paid dividends of $0.09 per share. What was the average annual growth rate of Intermark’s dividends from 2007 to 2011?
Suppose a stock has a current value of $50 per share and a dividend of $2 per share this year, and investors expect its dividends to grow at a rate of 3% per year. What is the return that investors
Consider two stocks: Company A stock and Company B stock. Investors require a return of 10% for each stock. Company A has a current dividend of $2.5 per share and investors expect its dividends to
Consider the following path of the stock price and dividends per share for the Comet stock: End of Year Price per Share Dividend per Share 2010 2011 $50 $60 2012 $55 053 $2 $3 $3 Complete the
Suppose you are evaluating an investment opportunity that requires a$1,000 investment today. Your return from this investment is $1,100 two years from today. What is the value of this investment
Suppose you are evaluating an investment opportunity that requires a$1,000 investment today. Your return from this investment is $1,100 two years from today. What is the return on this investment?
Consider an investment CCC, which has the following expected cash flows:What is CCC’s net present value and profitability index if the cost of capital is 6%?What is CCC’s internal rate of return?
Suppose you are evaluating investment DDD that has the following expected cash flows:What is DDD’s net present value and profitability index if the cost of capital is 5%?What is DDD’s internal
Suppose you are evaluating investment EEE, which has the following estimated cash flows:What is EEE’s net present value and profitability index if the cost of capital is 8%?What is EEE’s internal
Suppose you are evaluating investment FFF, which has the following anticipated cash flows:What is FFF’s net present value and profitability index if the cost of capital is 10%?What is FFF’s
Which investment, if any, would you choose if you are offered the following two investments?The cost of capital for both investments is 10%. Cash Flows Year A B Today -100 -100 1 80 0 2 120 210
Consider two investments, A and B:At what cost of capital does your preference for one investment change to prefer the other investment? Cash Flows Year A B Today -100 -100 1 80 0 2 120 210
If the profitability index of an investment is equal to 1.25 and the initial cash flow is $1,000 what is the investment’s net present value?
Consider two investments, C and D:Which investment is more profitable if the cost of capital of both investments is 8%? Cash Flows Year A B Today -100 1 -100 40 0 23 2 40 0 3 40 130
If you invest $10,000 in an account that pays 4% interest, compounded quarterly, how much will be in the account at the end of five years if you make no withdrawals?
If you invest $2,000 in an account that pays 12% per year, compounded monthly, how much will be in the account at the end of six years if you do not make any withdrawals?
Suppose you invest $3,000 in an account that pays interest at the rate of 8% per year, compounded semi-annually. How much will you have in the account at the end of five years if you do not make any
Suppose you invest $100 for 20 years in an account that pays 2% per year, compounded quarterly.a. How much will you have in the account at the end of 20 years?b. How much interest on interest will be
If you deposit $100 in an account that pays 4% interest, compounded annually, what is the balance in the account at the end of three years if you withdraw only the interest on the interest each year?
Suppose you invest €100 today in an investment that yields 5% per year, compounded annually. How much will you have in the account at the end of six years?
Which investment of $10,000 will provide the larger value after four years:a. Investment A earns 5% interest, compounded semiannually.b. Investment B earns 4.8% interest, compounded continuously.
What will be the value in an account at the end of 12 years if you deposit $100 today and the account earns 6% interest, compounded annually?
What will be the value in an account at the end of six years if you deposit $100 today and the account earns 12% interest, compounded annually?
What will be the value in an account at the end of 10 years if you deposit $1,000 today and the account earns 7% interest, compounded continuously?
Complete the following, solving for the present value, PV: Case Future Value Interest Rate Number of Periods Present Value A $10,000 5.0% 5 B 563,000 4.0% 20 C $5,000 5.5% 3
Suppose you want to have $0.5 million saved by the time you reach age 30, and suppose that you are 20 years old today. If you can earn 5% on your funds, how much would you have to invest today to
How much would I have to deposit in an account today that pays 12%interest, compounded quarterly, so that I have a balance of $20,000 in the account at the end of 10 years?
Suppose I want to be able to withdraw $5,000 at the end of five years and withdraw $6,000 at the end of six years, leaving a zero balance in the account after the last withdrawal. If I can earn 5% on
Using an interest rate of 5% per year, what is the value today of the following cash flows: Years from Today Cash Flow 123+ 0 0 3 10,000 4 10,000
Which of the following series has the highest present value, assuming an annual interest rate of 5%? End of First End of Second End of Third Series Year Year Year B AR A 0 0 500 165 165 165 C 470 0 0
What is the present value of $500 to be received in two years if the interest rate is 4% per year and: Compounds daily? Compounds continuously?
What is the present value of £5 million to be received in 10 years if interest is 12% compounded monthly?
What is the present value of $6,000 to be received in 10 years if interest is 6%, compounded continuously?
What is the present value of $10,000 to be received in three years if the interest rate is 5%?
What is the value at the end of 2009 of the following series of cash flows if the discount rate is 5%?
What is the value at the end of 2012 of the following series of cash flows if the interest rate is 5%?
What is the value today of a promised series of cash flows of $6,000 at the end of each of the next five years? Use a 10% discount rate. Year Cash Flow 2010 2011 $1,000 2012 $3,000 Year Cash Flow
What is the value today of the following series of cash flows if the discount rate is 10%? Years from Now Cash Flow 1. 0 2 0 34 10,000 4 10,000
Suppose you deposit $1,000 in an account at the end of each year for three years. If the account earns 5% interest per year, what is the balance in the account at the end of three years?
Calculate the present value of a four-payment $1,000 ordinary annuity if the interest rate is 5%.
Suppose you deposit $1,000 each year for three years in an account that pays 5% interest, compounded annually. If you make the deposits at the beginning of the year, what is the balance in the
Suppose you win $7 million Powerball lottery. You receive your lottery winnings in 20 equal annual installments, with the first installment paid immediately. If you could invest the funds to yield 5%
Consider an annuity consisting of three payments of $4,000 each. If the interest rate is 5% per year, what is the present value of this as:a. An ordinary annuity?b. An annuity due?c. A deferred
Your broker has proposed that you pay $50,000 today for an annuity of $5,000 per year for fifteen years. If your opportunity cost of funds is 6% and the returns from this investment are tax-free, is

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