Exam 5: Time Value of Money

Janice borrows $25,000 from the bank at 15 percent to be repaid in 10 equal annual installments.Calculate the end-of-year payment.

Congratulations! You have just won the lottery! However,the lottery bureau has just informed you that you can take your winnings in one of two ways.You can elect to receive a payment of $1,000,000 now or a payment of $1,750,000 in five years.Assume you can earn 5% on funds that you invest today.How much money would you have in five years if you take the immediate $1,000,000 payment and invest it? What does this tell you about the wisdom of selecting the immediate payment versus the future payment? Using the same 5% interest rate,what is the present value of the $1,750,000 that you could receive in five years? What does this calculation tell you about which lottery payout option you should choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a sports car from her friend,Jim.She has $2,500 now and would like to save equal annual end-of-year deposits to pay for the car.How much should she deposit at the end of each year in an account paying 8 percent interest to buy the car?

Find the equal annual end-of-year payment on $50,000,15 year,and 10 percent loan.

Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits.If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment,how much must each deposit be in order to accumulate the $40,000?

In general,with an amortized loan,the payment amount grows over the life of the loan,the principal portion of each payment grows over the life of the loan,and the interest portion declines over the life of the loan.

A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity.The rate of interest is expected to be 8 percent for all future time periods.How large must the endowment be?

Dorothy borrows $10,000 from the bank.For a four-year loan,the bank requires annual end-of-year payments of $3,223.73.The annual interest rate on the loan is ________.

The future value of an ordinary annuity of $2,000 each year for 10 years,deposited at 12 percent,is ________.

The time value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.

The process of taking cash flow that is received or paid in the future and stating that cash flow in present value terms is called discounting.

The future value of a dollar ________ as the interest rate increases and ________ the longer the money remains invested.

Entertainer's Aid plans five annual colossal concerts,each in a different nation's capital.The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity.The endowment will be given at the end of the fifth year.The rate of interest is expected to be 9 percent in all future periods.How much must Entertainer's Aid deposit each year to accumulate to the required amount?

The annual percentage yield (APY)is the effective rate of interest that must be disclosed to customers by banks on their savings products as a result of "truth in savings laws."

Nico is 30 years old and will retire at age 65.He will receive retirement benefits,but the benefits are not going to be enough to make a comfortable retirement life for him.Nico has estimated that an additional $25,000 a year over his retirement benefits will allow him to have a satisfactory life.How much should Nico deposit today in an account paying 6 percent interest to meet his goal? Assume Nico will have 15 years of retirement.Assume that he withdraws $25,000 at the end of each year during retirement.

Alexis owns stock in a company which has consistently paid a growing dividend over the last 10 years.The first year Alexis owned the stock,she received $4.50 per share and in the 10th year,she received $4.92 per share.What is the growth rate of the dividends over the last 10 years?

Bill plans to fund his individual retirement account (IRA)by contributing $2,000 at the end of each year for the next 20 years.If Bill can earn 12 percent on his contributions,how much will he have at the end of the twentieth year?

How many years would it take for Harry to save an adequate amount for retirement if he deposits $2,000 per month into an account beginning today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

Mr.& Mrs.Pribel wish to purchase a boat in 8 years when they retire.They are planning to purchase the boat using proceeds from the sale of their property which is currently worth $90,000 and its value is growing at 7 percent a year.The boat is currently worth $200,000 increasing at 5 percent per year.In addition to the value of their property,how much additional money should they deposit at the end of each year in an account paying 9 percent annual interest in order to be able to buy the boat upon retirement?

A certain investment promises to pay you $2,500 per year forever with the first payment starting next year.If you can earn a 5% return on similar investments,what's the most you would pay for this investment today?