Exam 3: The Time Value of Money Part 1

Your aunt 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?

Consider the TVM equation: A decrease in the time period will increase the future value, other things remaining equal.

For much of the 20th century, new car prices rose at an annual rate of 5.73%. Given a beginning new car price of $600, how long did it take for the average new car price to rise to $16,950? Please round to the nearest year.

Which of the following is the correct formula for calculating the future value?

Harold's parents have offered him a $10,000 high school graduation gift with an option for another $20,000 upon graduation from college in four years. His friends tell him this is a $30,000 gift from his parents, but Harold already knows something about the time value of money. If the expected inflation rate over the next four years is expected to be 4% per year, what does Harold think the gift is worth in today's dollars? How should he explain his thinking to his friends?

Your manufacturing firm has just secured a sale to the federal government with payment of $450,000 due in nine months. You have asked your bank for cash today with the stipulation that you will give the proceeds from the government contract to the bank in nine months. The bank has agreed to your request if you allow them to discount the cash flows at an annual rate of 8%. How much will the bank pay you today under this agreement?

You need $32,000 at the end of 6 years. If you can earn 0.625% per month, how much would you need to invest today to meet your objective?

In 1970, before the era of major league baseball free agency, the minimum player salary was $12,000. In 1975, the minimum salary was $16,000. What was the average annual growth in the minimum salary in major league baseball over those five years?

If interest rates are positive, then discounting increases the future value of an investment while compounding reduces the present value of an investment.

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?

The financial aid office at your university has offered to pay your full annual tuition cost of $22,000 this year, as long as you maintain a grade point average of 3.00. If tuition costs rise at a rate of 6% per year while you are in college, but the financial aid office continues to pay exactly $22,000 per year for your tuition, how much out-of-pocket tuition costs will you have your senior year? NOTE: Think carefully about this problem when figuring the number of years from the start of your freshman year to the start of your senior year, assuming normal progress toward graduation in four years. Further, be aware that while tuition costs are rising your tuition is covered up to only $22,000. You must pay any excess tuition costs.

What is the Rule of 72? Why do you think the Rule of 72 came into widespread use? Give an example of where you think the rule could be useful.

In your first year out of college you hope to earn $50,000 per year. How many years will you have to work until you earn $100,000 if your income increases at a rate of 10% per year? Use the Rule of 72 to determine your answer.

A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the following statements is true?

Madison is taking over as Chief Marketing Officer at MidWest Graphics. She has pledged to increase sales from their current level of $12,000,000 at a rate of 10% per year until the firm hits sales of $20,000,000 per year. How long will it take Madison to hit the target goal at this rate of increase?

Consider the TVM equation: An increase in the present value will decrease the future value, other things remaining equal.

You currently have $2,500 invested at an annual rate of 8%. How long will it take for this investment to grow to a value of $3,500?

Jasmine 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 Jasmine 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?

Given an interest rate of 0%, the present value of $1,500 to be received 5 years in the future is less than $1,500.

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