Chapter 3: Time Value of Money

Lance has $3,500 but needs $7,000 to purchase a new golf cart. If he can invest his money at a rate of 12% per year, approximately how many years will it take the money in Lance's account to grow to $7,000? Use the Rule of 72 to determine your answer.

6 years

Buying your own home is often mentioned as "the best investment you can make." In 1964, the average home sale price was $19,600. By 2009, the average home sale price had risen to $272,900. What was the average annual rate of change in the price of houses over this 45 year time period?

6.03% per year

The question "How long will I have to wait to reach a certain future value?" is best answered by which form of the TVM equation?

n = ln(fv/pv) / ln(1+r)

You can invest your money at a rate of 7% per year. At this rate it will take you just over ________ years to double your money. Use the Rule of 72 to determine your answer.

10

If you can earn 5.25% per year on your investments, how long will it take to double your money?

13.55 years

Median U.S. wages in 2014 were $53,675, compared to the median wage in 1990 of $28,960. What was the average annual increase in median wages over this 24-year period?

2.60%

You gave your little sister two rabbits for Easter three years ago and now she has 64 of the cute little bunnies. What is the average annual rate of increase in the number of rabbits your sister owns? Note: Your parents are not very pleased with you right now.

217.5% finding the rate

Your grandfather likes to tell the story about how he started his ranch with 100 head of cattle and grew the ranch to 2,500 head of cattle. He said "My plan was simple: grow the number of head of cattle at a rate of 10% per year." How long did it take him?

33.77 years

Five years ago, Maria's annual salary was $73,500. Today, she earns $91,900. What has been the average annual percentage rate of growth of Maria's salary?

4.57% (91,900/73,500)^1/5 = because you are looking for rate

You currently have $3,500 invested at an annual rate of 8%. How long will it take for this investment to grow to a value of $5,000?

4.63 years

You have saved $1,250 for a used motorcycle that has a current price of $1,550. If your money is sitting in an account earning 2.25% per year, how long will it take for this account to grow to $1,550? Note: The motorcycle's price may have changed by the time your account reaches a value of $1,550.

9.67 years

Your manufacturing firm has just secured a sale to the federal government with payment of $480,000 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 6%. How much will the bank pay you today under this agreement?

$459,475

An investment promises a payoff of $995 two and one-half years from today. At a discount rate of 4.5% per year, what is the present value of this investment?

$891.32

Your parts supplier gives you one-quarter of a year to pay for parts ordered today, or offers you a discount if you pay cash at purchase. You have just purchased $94,500 worth of parts from your supplier and the discount is at an annual rate of 10%. How much will you pay for the parts if you pay today?

$92,275

The current price on a 60-inch flat panel LCD HD television is $1,200. Big screen HD television prices have dropped at an average rate of 12% per year in recent years. If you expect this trend to continue, how much will this style of television cost in two years?

$929

In the equation r = (FV/PV)1/n - 1, the r is sometimes referred to as the ________.

All of these

Which of the following investments has a larger future value: Investment A, a $1,000 investment earning 5% per year for 6 years, or Investment B, a $500 investment earning 10% per year for 6 years, with a bonus of an extra $500 added at the end of the sixth year?

Investment B, with a future value of $1,386.

A two-year investment of $3500 is made today at an annual interest rate of 5.75%. Which of the following statements is TRUE?

The future value would be greater if the interest rate was higher.

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?

The principal is $13,000, the time period is 5 years, the future value is $18,233.17, and the interest rate is 7%.

Your grandparents leave on their dream vacation to Antarctica in three years. The cruise vacation will cost them $24,000. If they have already saved $22,500 and are investing it at a rate of 2.50% per year, will they have saved enough money for their trip?

Yes, to have enough money they would have already needed to save $22,286.39 and they already exceed that amount.