FRL 3000 chapter 5 time value of money, single cash flow
If $100 earns compound interest for 2 years at 10 percent per year, the future value will be ____.
$121.00 Reason: FV = $100 × 1.10 2 = $121
You invest $500 at 10 percent interest. At the end of 2 years with simple interest you will have ____ and with compound interest you will have ____.
$600; $605 Reason: With simple interest you will earn $500 X 0.10 = $50 each year. Your total will be $500+100=$600. With compound interest, you will have $500(1.10)2 = $605 at the end of the two years. Given the same rate of interest, the FV will always be higher with compound interest.
Which formula below represents a present value factor?
1/(1 + r)^t
_______value is the cash value of an investment at some time in the________
future; future
The greater the number of time periods, the (smaller/greater) the impact of compounding.
greater
Longer-term bonds have (smaller/greater) interest rate sensitivity because a (smaller/larger) portion of a bond's value comes from the face amount.
greater, larger, or higher; larger, greater, or higher
The reason that interest rate risk is greater for Blank______ term bonds than for Blank______ term bonds is that the change in rates has a greater effect on the present value of the Blank______ than on the present value of the Blank______.
long; short; face value; coupon payments
The basic present value equation underlies many of the _____.
most important ideas in corporate finance Reason: The basic present value equation underlies many of the most important ideas in corporate finance.
The two major forms of long-term debt are ______ issue and privately placed.
public
Suppose present value is $100, future value is $1,000, and N is 10 years. Which formula below is used to find the (decimal) interest rate?
r = (1000/100)(1/10) - 1
Interest earned only on the original principal amount invested is called
simple
The (smaller/greater) the interest rate changes, the greater the impact to the future value of an amount invested.
greater
The _______ value is the current value of future cash flows discounted at the appropriate discount rate.
present
If you want to know how much you need to invest today at 12 percent compounded annually in order to have $4,000 in five years, you will need to find a(n) _______ value.
present Reason: If you want to know how much you need to invest today at 12% compounded annually in order to have $4,000 in five years, you will need to find a present value.
If we know the interest rate is 10 percent per year and the money is invested for 10 years, then we can use the _____ to find the present value.
present value factor
The discount rate is also called the rate of
return
Interest earned on the original principal amount invested is called _____.
simple interest
Suppose you want to save $10,000 to buy a car. You have $6,000 to deposit today and you can earn 6% on your investments. You want to know when you'll have enough to buy the car. Which of the following spreadsheet functions will solve the problem?
=NPER(0.06,0,−6000,10000) Reason: Unlike in the financial calculator, you must enter the interest rate in decimal form (0.06) to solve using a spreadsheet. Like in the financial calculator, you must put a negative sign on either the PV or the FV.
Which formula will you enter into a spreadsheet cell to determine how long it will take $40 to grow to $240 at an interest rate of 6.53% compounded annually?
=NPER(0.0653,0,−40,240)
Which of the following methods can be used to calculate present value?
A financial calculator A time value of money table An algebraic formula
Which of the following can be determined using the future value approach to compound growth developed in this chapter?
Dividend growth Sales growth
Which of the following is the correct mathematical formula for calculation of the future value of $100 invested today for 3 years at 10% per year?
FV = $100 × (1.10)3
Which of the following investments would result in a higher future value?Investment A - 12% APR for 10 years investment B - 12% APR for 12 years
Investment B Reason: Because the rates are the same, investment B would give a higher future value because on additional period of interest is earned.
The basic present value equation is:
PV = FVt/(1 + r)^t
What are the two major forms of long-term debt?
Public issue and privately placed
What is the future value of $100 compounded for 50 years at 10 percent annual interest?
Reason: FV = $100 × 1.1050 = $11,739.09
When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year.
The Same
The formula for a present value factor is 1/(1+r)^t True Reason: This is the present value interest factor, not the present value itself. In order to get PV, you need to multiply FV by this factor. Notice how as the denominator becomes larger due to higher interest or longer periods, it reduces the factor.
True Reason: This is the present value interest factor, not the present value itself. In order to get PV, you need to multiply FV by this factor. Notice how as the denominator becomes larger due to higher interest or longer periods, it reduces the factor.
True or false: Given the same rate of interest, more money can be earned with compound interest than with simple interest.
True Reason: With compound interest, you earn interest on interest as well as interest on the principal.
Future value is the Blank______ value of an investment at some time in the future.
cash
The idea behind ______ is that interest is earned on interest.
compound
If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?
FV = $100 × 1.103 = $133.10
True or false: Small changes in the interest rate affect the future value of a small-term investment more than they would affect the value of a long-term investment.
False Reason: Small rate differences can be worth thousands of dollars, especially when either the amount or the time period is large.
True or false: The multi-period formula for future value using compounding is FV = (1 + r)t.
False Reason: FV = PV × (1 + r)t
The process of leaving your money and any accumulated interest in an investment for more than one period, thereby reinvesting the interest, is called
compounding or compound