Deck 27: The Time Value of Money: Future Amounts and Present Values Answer Key

Question 1

The future value of an investment gradually increases toward the present amount.

Answer 1

False

Question 2

The obligation for deferred income taxes is the only long-term liability that is not reported at its present value.

Answer 2

True

Question 3

The present value of an ordinary annuity is the amount that equals payments made at the end of successive equal periods is worth today.

Answer 3

True

Question 4

Discounting a future amount of a cash receipt will determine the present value of that receipt.

Question 5

The present value of an annuity is calculated by multiplying the periodic cash flows by the discounted factor from the future value of an annuity table.

Question 6

If you invested $10,000 at 6% on your 20^th birthday how much would you have on your 40^th birthday?

A) $32,071.40.
B) $31,180.00.
C) $36,785.59.
D) $12,158.12.

Question 7

Future value is the amount that must be invested today at a specific interest rate to receive a particular amount at some future date.

Question 8

The future amount of an annuity is calculated by multiplying the periodic payment amount by the discounted factor from the future value of an annuity table.

Question 9

The rate of interest is usually expressed as an annual rate.

Question 10

As the discount rate required by an investor increases, the present value of an investment decreases.

Question 11

An annuity due assumes the cash flow will occur at the beginning of the period.

Question 12

An interest rate of 12% a year is the same as 6% for 2 months.

Question 13

Annuities may provide equal amounts to an investor at fixed periods of time over the life of an investment.

Question 14

The lower the discount rate of an investment, the lower the present value of the investment.

Question 15

The future amount of an annuity is calculated by multiplying the present value of the annuity by its applicable factor from a table.

Question 16

The market price of a bond is equal to its present value.

Question 17

If I invest $20,000 at 2.5% today, how long will it take to reach a minimum of $50,000 compounded semi-annually?

A) 5 years.
B) 19 years.
C) 9 and ½ years.
D) 17 years.

Question 18

The present value of a single amount can only be calculated through the application of complex calculations.

Question 19

Compounding interest assumes the interest on an investment is reinvested.

Question 20

The present value of a single amount is calculated by multiplying the future amount by the present value of $1 table.

Question 21

To determine the amount to be deposited in a bank today to grow to $5,000 three years from now at 7% which table should be used?

A) Present value of 1.
B) Future value of 1.
C) Present value of an annuity.
D) No table is required, just multiply $5,000 by 1.07.

Question 22

The future value of an annuity is:

A) Always more than the present value.
B) Always less than the present value.
C) Equal to the present value.
D) Double the present value.

Question 23

Anthony Driver wants to buy a new car in 4 years. He knows that he can earn 6% interest compounded semi-annually. How much must he deposit now in order to have $26,000 at the end of 4 years?

A) $21,390.20.
B) $20,524.66.
C) $38,413.96.
D) $31.603.26.

Question 24

Financial instruments are recorded at:

A) Future values.
B) Present values plus interest.
C) Present values less interest.
D) Present values.

Question 25

A scholarship fund has $75,000 to invest now to provide scholarships to high school students. They want to have at least $150,000 in 8 years. What rate of interest must they invest this money at to reach their goal?

A) 8%.
B) 9%.
C) 10%.
D) 11%.

Question 26

To determine the present value of a single amount to be received or paid at a future time you need to know all of the following except:

A) The interest rate or discount rate.
B) The number of periods.
C) The future value.
D) The time between periods.

Question 27

The present value of an investment is:

A) The amount an investor would pay today to receive a certain amount in the future.
B) The amount an investor would pay today plus the interest the investor would expect to receive a certain amount in the future.
C) The amount an investor would pay today less the interest the investor requires.
D) 90% of the future value of an investment.

Question 28

Your wealthy aunt wishes to give you a trip to Paris when you graduate from college in three years. She estimates the trip will cost $4,000. How much must she invest now at 4% to accumulate enough for you to take this trip?

A) $3,287.72.
B) $3,556.00.
C) $4,499.44.
D) $3,161.24.

Question 29

Compound interest:

A) Is interest only on the principal amount for several years.
B) Is interest on the principal and previously earned interest.
C) Is interest only on previous interest excluding the principal.
D) Is equal to simple interest received for several years.

Question 30

A note that does not include an interest rate should be recorded at:

A) Its face amount if the difference between face and present value is material.
B) Its present value if the difference between face and present value is material.
C) Its face amount at all times.
D) Its present value at all times.

Question 31

How much must I invest today in order to have $25,000 in 5 years assuming 12% interest compounded annually?

A) $14,185.75.
B) $15,888.00.
C) $18,681.50.
D) $17.624.00.

Question 32

If I invest $50,000 today for 5 years and it grows to $84,253, what rate of interest have I received?

A) 5%.
B) 6%.
C) 11%.
D) 12%.

Question 33

Joe Notsosmart invested $10,000 at 8% simple interest for 5 years. How much more would he have received if he had received compound interest annually at the same rate?

A) $4,000.
B) $4,693.
C) $693.
D) $400.

Question 34

The time value of money is based on the idea that:

A) The value of money in the future equals the interest received in the present.
B) The value of money in the future will be greater than an amount available today.
C) The value of money at present over some length of time will be reduced by inflation.
D) The future value of money will become the current value as time passes.

Question 35

The present value of a cash amount:

A) Is always less than the future value.
B) Is always more than the future value.
C) Is the same as the future value.
D) Is the same as the actual cash value.

Question 36

If you receive $20,000 as a gift and invest it at 12% compounded quarterly, how much will you have at the end of three years?

A) $32,020.60.
B) $28,515.20.
C) $22,497.20.
D) $14,027.60.

Question 37

The difference between the present value and the future value of a sum of money depends upon:

A) The rate of interest.
B) The length of time.
C) The rate of interest and the length of time.
D) Neither the rate of interest nor the length of time.

Question 38

If I invest $100 at the end of each year for four years at 6% how much will I have at the end of the fourth year?

A) $421.24.
B) $437.46.
C) $563.71.
D) $432.95.

Question 39

Judy Bright has just won the lottery. She can elect to receive her winnings in equal payments of $200,000 a year for the next ten years on December 31 or to receive $2,000,000 immediately. If the current interest rate is 6%, which choice will provide the highest amount:

A) Receiving $2,000,000 immediately.
B) Taking equal payments for 10 years.
C) It does not matter since either choice provides the same amount.
D) Refusing to accept the winnings since it is not enough.

Question 40

Financial instruments do not include:

A) Contracts that call for receipts or payment of cash.
B) Equity investment in another business.
C) Cash.
D) Tangible assets.

Question 41

Use the tables to determine the answers to the following:
(1) How much must be invested now for 5 periods at 6% to amount to $15,000?
(2) How much is $3,000 invested now at 8% in 8 periods worth?
(3) How much is $25,000 compounded quarterly at 12% for 4 years?

Question 42

Explain what is meant by the "time value of money." Provide examples.

Question 43

Powers Company wishes to issue $2,000,000 of 8%, 10 year bonds which pay interest semi-annually. The current discount rate is 6%. What amount should the bonds sell for?

Question 44

(a) How long will it take Barbara to accumulate $30,000 to buy a car if she invests $15,000 at 5%? (b) How long will it take if she invests the same amount at 4% semi-annually?

Question 45

Belle invests $200 at the end of each year in a savings account which pays 5% annually. How much will Belle have at the end of 5 years?

A) $1,000.
B) $1,105.13.
C) $1,077.50.
D) $1,082.37.

Question 46

A future amount is the dollar amount to which a present value will ______________ over time.

A) vanish.
B) accumulate.
C) disappear.
D) remain.

Question 47

Joan is 75 years old and wishes to retire. She needs to have $48,000 a year plus her social security to live in the style she is accustomed to. She would like to have enough money in her retirement account which earns 5% compounded annually to support her for the next 15 years. How much must be in the fund if she takes the first payment at year-end?

Question 48

Explain how compound interest applies to the time value of money.

Question 49

Sam Rivers has $3,000 to invest. He must decide whether to invest this money for five years at 10% compounded semi-annually or at 12% compounded annually. Which option should he select?