Chapter 5

If you want to have $150,000 in 2 years, how much do you need to put in a savings account today that pays 5% compounded annually? (Do not round your intermediate calculations and final answer.)

$136,054.42 Future value = Present value × (1 + interest rate)n; $150,000 = PV × (1.05)2; $150,000 = PV × 1.1025; PV = $150,000 / 1.1025; PV = $136,054.42

The future value of $200,000 invested at a 7% annual rate, compounded quarterly for 3 years is _____. (Do not round your intermediate calculations. Round the final answer to the nearest two decimal places.)

$246,287.86 Future value = Present value × (1 + interest rate)n; FV = $200,000 × (1 + 0.07/4)(4×3); $200,000 × (1.0175)12; $200,000 × 1.2314; FV = $246,287.86

Castelda company issues zero coupon bonds which mature in 30 years. These bonds can be bought for $999.38 and then pay no annual interest payments, only $100,000 at maturity. What is the annual percentage cost of these bonds to the issuing company? (Do not round intermediate calculations. Round your final answer to two decimal places of percentage.)

16.59% Future value = Present value × (1 + interest rate)n; $100,000 = $999.38 × (1 + i)30; i = 16.59%

At what rate must $4,000 be compounded annually for it to increase to $40,000 in 15 years? (Do not round the intermediate calculations. Round the final answer to the nearest two decimals.)

16.59% Future value = Present value × (1 + interest rate)n; $40,000 = $4,000 × (1 + i)15; (1 + i)15= $40,000 / $4,000; (1 + i)15 = 10 - 1; (1 + i)15 = 10 - 1; (100.6666) - 1; r = 1.1659 - 1; Rate = 16.59%

Using the "Rule of 72", about how long will it take to double your money if you can expect to earn 9% per year?

8 years TDM = 72 / i; TDM = 72 / 9; TDM = 8 years

Why do earnings from compounding drive much of the return earned on a long-term investment?

A longer investment period will result in a greater proportion of total earnings from interest earned on interest.

Which of the following situations will result in an increase in the future value of an investment?

An increase in the rate of interest

Which one of the following processes do we use when calculating the price of an asset?

Discounting.

Which of the following statements is true about the compound factor?

The compound factor decreases as the number of periods increase.

The future value of an investment will be larger if the investment is for 12 years instead of 6 years. Which of the following statements is true about the future value of an investment?

The future value of an investment will be larger if the investment is for 12 years instead of 6 years.

Assume that potential projects X, Y and Z will each pay a total of $100,000 over 20 years. X pays $8,000 per year for 10 years and $2,000 per year for 10 years. Y pays $2,000 per year for 10 years and $8,000 per year for 10 years. Z pays $5,000 per year for 20 years. Which project is likely to be most attractive to an investor?

The project with large cash flows early is likely to be most attractive.

Which of the following is a similar concept to the compound growth rate of money?

The yield on a bond

Which of the following statements best describes time lines?

Time lines are an important tool for analyzing problems that involve cash flows over time.

Under which of the following discounting methods will the present value of an investment be the highest, assuming the same annual interest rate?

Yearly

Principal may be described as the _____.

beginning balance in a savings account

The customer benefits from arranging financing through the dealer because the

customer often gets to drive the car home that day.

By paying off the manufacturer in 15 days rather than a year, the dollar carrying cost of the car to the dealership is

decreased.

The present value of future cash flows:

increases as the discount rate decreases.

The difference between the value of new cars and the value of pre-owned cars is that

new cars tend to hold their value until the next model year, while pre-owned cars depreciate as long as they stay in inventory.

The time-value-of-money concept assumes that:

people accept less money to reduce the time they must wait.

Money has time value because:

people can earn interest on money that is invested.

Floor planning refers to the

relationship with banks that allows the dealer to help customers arrange financing.

Total compound interest is the:

sum of simple interest and the interest on interest

Generally, the future value of an investment will be greater if:

the investment is compounded at a higher rate of return.

The cost of a new car to the dealership is calculated as

the wholesale price from the manufacturer plus the carrying cost.