Chapter 5

What is the future value of $100 compounded for 50 years at 10 percent annual interest?

$11,739.09 FV = $100 × 1.1050 = $11,739.09

If you invest $100 at 10 percent compounded annually, how much money will you have at the end of 3 years?

$133.1 100x(1.1^3) FV = $100 × 1.10^3 = $133.10 (compound)

What is the future value of $1,000 invested for 8 years at 6%?

$1593.85 In the financial calculator, enter 1000 for PV, 8 for n, and 6 for I/Y. Solve for FV.

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

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

The multi-period formula for future value using compounding is FV = (1 + r)^t.

False It is FV = PV × (1 + r)^t

True or false: The multi-period formula for future value using compounding is FV = (1 + r)t.

False Missing PV! FV = PV × (1 + r)t

___ value is the cash value of an investment at some time in the___

Future ; future

The basic present value equation is:

PV = FVt/(1 + r)^t

The (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

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 concept of the time value of money is based on the principle that a dollar today is worth __________ a dollar promised at some time in the future.

more than

The basic present value equation underlies many of the _____.

most important ideas in corporate finance

In 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

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

The discount rate is also called the rate of ___

return

Interest earned on the original principal amount invested is called

simple interest

The difference between _______ interest and compound interest is that the amount of compound interest earned gets (bigger or smaller) ___________ every year.

simple; bigger

When the future value formula is used to calculate growth rates, the assumption is that _____ growth rate is achieved each year.

the same

Interest earned only on the original principal amount invested is called ___ interest.

simple

Which of the following can be determined using the future value approach to compound growth developed in this chapter? Multiple select question. Erratic growth Sales growth Dividend growth

Sales growth Dividend growth

If you invest for a single period at an interest rate of r, your money will grow to ______ per dollar invested.

(1+r) If you invest for a single period at an interest rate of r, your money will grow to (1 + r) per dollar invested.

Using a time value of money table, what is the future value interest factor for 10 percent for 2 years?

1.21 Look under 10% until you get to 2 for two years. That number is 1.10.

Which formula below represents a present value factor? 1/(1 + N)^r (1 + r)/t 1/N + 1/r 1/(1 + r)^t

1/(1 + r)^t

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. Like in the financial calculator, you must put a negative sign on either the PV or the FV.

Which of the following methods can be used to calculate present value? Multiple select question. A financial calculator Random number generation An algebraic formula A time value of money table

A financial calculator An algebraic formula A time value of money table

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: Discounting is the opposite of compounding.

True Compounding converts the present value into future value and discounting converts the future value into present value.

The formula for a present value factor is 1/ (1+r)^t

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

Discounting is the opposite of ___

compounding

The idea behind ______ is that interest is earned on interest.

compounding

The ___ rate is the rate used to calculate the present value of the future cash flows.

discount

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 are correct spreadsheet functions? Multiple select question. Discount rate = RATE(nper,pmt,pv,fv) Future value = FV(rate,nper,pmt,pv) Present value = PV(rate,nper,pmt,fv) Interest rate = DISCOUNT(nper,pmt,pv,fv)

Discount rate = RATE(nper,pmt,pv,fv) Future value = FV(rate,nper,pmt,pv) Present value = PV(rate,nper,pmt,fv)

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 FV = $100 × 0.10 × 3 FV = $100 × (1.10)^3 FV = $100 × 1.10 × 3

FV = $100 × (1.10)^3

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

Calculating the present value of a future cash flow to determine its value today is called _____.

discounted cash flow valuation