FIN 3123 Chp 5 Smartbook
n general, if you invest for one period at an interest rate of r, your investment will grow to 1 (minus/plus) r
plus
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
The ________ value is the current value of future cash flows discounted at the appropriate discount rate.
present
The equation that results in the _______ value interest factor for a single deposit is as follows: 1/(1+r)^t
present
What is the future value of $1,000 invested for 8 years at 6%?
$1,593.85 In the financial calculator, enter 1000 for PV, 8 for n, and 6 for I/Y. Solve for FV.
What is the future value of $100 compounded for 50 years at 10 percent annual interest?
$11,739.09
If you invest for a single period at an interest rate of r, your money will grow to ______ per dollar invested.
(1+r)
Which formula below represents a present value factor?
1/(1 + r)^t
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
The basic present value equation is:
PV = FVt(1+r)t
Discounting is the opposite of
compounding
Using a time value of money table, what is the future value interest factor for 10 percent for 2 years?
1.21
Assuming the interest rate offered for a 10-year investment plan is same as for a 4-year investment plan. For an investor to achieve the same future value, which of these two plans would require a smaller savings amount to be deposited today?
10-year investment
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) Unlike in the financial calculator, you must enter the interest rate in decimal form (0.06) to solve using a spreadsheet.
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 investments would result in a higher future value?Investment A - 12% APR for 10 yearsInvestment B - 12% APR for 12 years
Because the rates are the same, investment B would give a higher future value because on additional period of interest is earned.
If $100 earns compound interest for 2 years at 10 percent per year, the future value will be
FV = $100 × 1.10 2 = $121
True or false: The multi-period formula for future value using compounding is FV = (1 + r)t.
False
True or false: When using the time value of money features of a financial calculator, you should key in the interest rate as a decimal.
False
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 Small rate differences can be worth thousands of dollars, especially when either the amount or the time period is large
_________ value is the cash value of an investment at some time in the __________
Future Future
Which of the following are correct spreadsheet functions?
Present value = PV(rate,nper,pmt,fv) Discount rate = RATE(nper,pmt,pv,fv) Future value = FV(rate,nper,pmt,pv)
Why is a dollar received today worth more than a dollar received in the future?
Today's dollar can be reinvested, yielding a greater amount in the future.
True or false: Given the same rate of interest, more money can be earned with compound interest than with simple interest.
True
True or false: The correct future value interest factor in a time value of money table for $1 in 10 years at 10 percent per year is 2.5937.
True
True or false: The formula for a present value factor is 1(1+r)t11+rt.
True 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.
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 ____.
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.
Future value is the ________ value of an investment at some time in the future.
cash
The idea behind ______ is that interest is earned on interest.
compounding
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
The _______ rate is the rate used to calculate the present value of the future cash flows.
discount
Calculating the present value of a future cash flow to determine its value today is called _____.
discounted cash flow valuation
The equation that results in the _______ value interest factor for a single deposit is as follows: (1 + r)t
future
The greater (smaller/greater) the interest rate changes, the greater the impact to the future value of an amount invested.
greater
The greater the number of time periods, the (smaller/greater) the impact of compounding.
greater
A dollar received one year from today has _____ value than a dollar received today.
less
All else equal, the longer time period you have before you will need the money, the (less/more) you will need to deposit today to have the same amount in the future.
less
The basic present value equation underlies many of the _____.
most important ideas in corporate finance
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
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
Fill in the blank question. The discount rate is also called the rate of ______
return
Interest earned only on the original principal amount invested is called _______ interest
simple
When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year.
the same