Exam 3: The Time Value of Money Part 1

Consider the TVM equation: The future value is always greater than the present value,even if the interest rate is negative.

Which of the following will result in a future value greater than $100?

Your finance professor suggests that you should have $2,500,000 in your retirement portfolio before you even THINK about retiring.Recently,your uncle sold valuable California real estate and handed you a check for $300,000.(This is the amount you have after paying taxes.He is now your favorite uncle. )How much of the $300,000 must you set aside today if you invest a portion of the money at an annual rate of 8.0% and you wish to retire in 35 years with the amount suggested by your finance professor?

In two years Boris plans to enroll at Cleese University,a prestigious university in the Pacific Northwest of the USA.If the current tuition is $23,500 per year and is expected to increase at a rate of 6% per year,how much will Boris pay in tuition his first year of school? (His first tuition payment is exactly two years from today. )In his fourth year? (His last tuition payment is exactly 5 years from today)(Rounded to the nearest dollar. )

You have just won the university lottery.If you graduate,you will receive a refund equal to the amount of tuition you paid in your first four years of school.However,you need money now and a firm that specializes in buying expected future cash flows has offered to discount the lottery winnings at a rate of 8% and pay you cash today in exchange for your future lottery winnings.Since you have studied finance,you insist that they discount the cash flows at 12% instead of 8% because there is some risk as to the certainty of your graduating.If the firm agrees to your demand,then this means they will increase the present value of what they will pay you today.

Olivia and her spouse have saved $4,500 for a 12-day cruise vacation in Europe.The couple needs $5,000 for a "nice" cabin or $6,000 for a "luxury" cabin.If cabin prices are expected to remain constant for the next three years and Olivia expects to earn 6% per year on her investments,will the couple's savings be enough to afford the "nice" cabin in three years? Can they afford the luxury cabin? Why or why not?

Your parents plan to spend $20,000 on a car for you upon graduation from college.If you will graduate in three years and your parents can earn 4.125% annually on their investment,how much money must they set aside today for your car?

Your grandmother places $13,000 into an account earning an interest rate of 7% per year.After 5 years the account will be valued at $18,233.17.Which of the following statements is correct?

Compare and contrast the discount rate with the compound (or growth)rate.

A plant nursery pays $2,000 for 800 one-gallon flowering trees,plants them,and forgets them.Five years later,the nursery is able to sell each of the 100 trees that survived for $50 each.What is the rate of return on its total investment?

If your bank offers a 5% annual rate of return compounded annually,then at the end of one year your $1,000.00 deposit would grow by $50.00 to $1,050.00.However,in the second year,your deposit would increase by $52.5025 to a total ending value of $1,102.50.Explain why the second year earns more interest on the investment than the first year.

You win the $5,000,000 lottery that pays you $250,000 per year over a 20-year period.Given negative interest rates,the lottery has a present value that is less than $5,000,000.

Even if you are given a present value,a single future value,and a time period,solving for the rate of return,r,is still a trial-and-error process.

In 1930,the highest paid player in major league baseball was Babe Ruth of the New York Yankees,with an annual salary of $80,000.In 2005,the highest paid player in major league baseball was Alex Rodriguez,also of the New York Yankees,with a salary of $25,000,000.What was the average annual rate of growth in the top baseball salary over this time period?

In 1975,the era of major league baseball free agency began.The average player salary was $16,000.In 1980,the average salary was $30,000.What was the average annual growth in the minimum salary in major league baseball over those five years?

$1,000 received 5 years from today discounted at an annual rate of 10% has a smaller present value than $1,000 received 10 years from today discounted at an annual rate of 5%.

The Rule of 72 is a rule of thumb for estimating the length of time necessary to double your money,given an interest rate.

________ is simply the interest earned in subsequent periods on the interest earned in prior periods.

In your first year out of college you hope to earn $60,000 per year.How many years will you have to work until you earn $120,000 if your income increases at a rate of 10% per year? Use the Rule of 72 to determine your answer.

Consider the TVM equation: Present values and interest rates are inversely related.