Question 1

An annuity with an infinite life is called a(n)________.

Accepted Answer

An annuity with an infinite life is called a perpetuity.

Question 2

The annual rate of return is referred to as the ________.

Accepted Answer

The annual rate of return is often referred to as the discount rate, especially in contexts involving the present value of future cash flows or investments.

Question 3

An annuity due is a stream of equal cash flows with each cash flow arriving at the beginning of each period.

Accepted Answer

An annuity due is a type of annuity where payments occur at the beginning of each period, rather than at the end, as in a regular annuity. Both regular and annuity due involve a stream of equal cash flows, but the timing of the cash flows differs.

Question 4

An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.

Accepted Answer

An ordinary annuity is an annuity in which cash flows occur at the end of each period, while an annuity due is an annuity in which cash flows occur at the beginning of each period.

Question 5

A(n)________ is an annuity with an infinite life making continual annual payments.

Accepted Answer

A perpetuity is an annuity with no end date, meaning it makes continuous payments forever. The other answer choices are not related to perpetuities.

Question 6

Congratulations! You have just won the lottery! However,the lottery bureau has just informed you that you can take your winnings in one of two ways.You can elect to receive a payment of $1,000,000 now or a payment of $1,750,000 in five years.Assume you can earn 5% on funds that you invest today.How much money would you have in five years if you take the immediate $1,000,000 payment and invest it? What does this tell you about the wisdom of selecting the immediate payment versus the future payment? Using the same 5% interest rate,what is the present value of the $1,750,000 that you could receive in five years? What does this calculation tell you about which lottery payout option you should choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

Accepted Answer

The answer of Congratulations! You have just won the lottery!...

Question 7

Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years.

Accepted Answer

The answer of Calculate the future value of $4,600 received...

Question 8

Dan and Jia are have just purchased a condominium for $70,000.Since the condo is very small,they hope to move into a single-family house in 5 years.How much will their condo be worth in 5 years if inflation is expected to be 8 percent?

Accepted Answer

The answer of Dan and Jia are have just purchased...

Question 9

In comparing an ordinary annuity and an annuity due,which of the following is TRUE?

Accepted Answer

The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity due to the fact that payments are made at the beginning of each period and have a longer time to compound. Therefore, option A is the correct choice. Option B is false, and Option C is incorrect because it confuses the present value with the future value. Option D is also incorrect because receiving payments earlier may be more valuable to some individuals.

Question 10

Colin has inherited $6,000 from his grandmother.He would like to invest this money for two years and then use the proceeds from that investment to buy a new high-end gaming computer for $7,000.Will Colin have enough money to buy the computer if he deposits his money in an account paying 8 percent compounded semiannually?

Accepted Answer

The answer of Colin has inherited $6,000 from his grandmother.He...

Question 11

Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually.She plans to leave the funds in this account for seven years earning interest.If the goal of this deposit is to cover a future obligation of $65,000,what recommendation would you make to Aunt Tillie?

Accepted Answer

The answer of Aunt Tillie has deposited $33,000 today in...

Question 12

The present value of a $20,000 perpetuity at a 7 percent discount rate is ________.

Accepted Answer

The formula for present value of a perpetuity is PV = C/r, where C is the cash flow and r is the discount rate. Plugging in the values, we get PV = $20,000/0.07 = $285,714. Therefore, the correct answer is B.

Question 13

The present value of a $25,000 perpetuity at a 14 percent discount rate is ________.

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = P / r, where PV is the present value, P is the payment per period, and r is the discount rate. Here, P = $25,000 and r = 0.14. Thus, PV = $25,000 / 0.14 = $178,571.

Question 14

Calculate the present value of $89,000 to be received in 15 years,assuming an opportunity cost of 14 percent.

Accepted Answer

The answer of Calculate the present value of $89,000 to...

Question 15

The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero.

Accepted Answer

This is true because in an annuity due, each payment is made at the beginning of the period and earns interest for the entire period, while in an ordinary annuity, each payment is made at the end of the period and earns interest for one less period. This means that each payment in an annuity due has one more period to accumulate interest, resulting in a higher future value.

Question 16

Which of the following is TRUE of annuities?

Accepted Answer

An annuity due is a stream of cash flows with payments made at the beginning of each period, while an ordinary annuity has payments made at the end of each period. The statements in choices A and D are incorrect, and choice B describes a growing annuity, not a regular annuity.

Question 17

China Manufacturing Agents,Inc.is preparing a five-year plan.Today,sales are $1,000,000.If the growth rate in sales is projected to be 10 percent over the next five years,what will the dollar amount of sales be in year five?

Accepted Answer

The answer of China Manufacturing Agents,Inc.is preparing a five-year plan.Today,sales...

Question 18

Bill plans to fund his individual retirement account (IRA)by contributing $2,000 at the end of each year for the next 20 years.If Bill can earn 12 percent on his contributions,how much will he have at the end of the twentieth year?

Accepted Answer

Using the future value formula: FV = PMT x (((1 + r)^n - 1) / r)
where PMT = $2,000, r = 12%, and n = 20.
FV = $2,000 x (((1 + 0.12)^20 - 1) / 0.12) = $144,105. Therefore, the answer is (D).

Question 19

Your current income is $50,000 per year,and you would like to maintain your current standard of living (i.e.,your purchasing power)when you retire.If you expect to retire in 30 years and expect inflation to average 3% over the next 30 years,what amount of annual income will you need to live at the same comfort level in 30 years?

Accepted Answer

To maintain the same purchasing power in 30 years, you need to adjust your current income for inflation. The formula to calculate the inflation-adjusted income is:

Inflation-adjusted income = Current income x (1 + inflation rate)^number of years

In this case, the inflation-adjusted income you need in 30 years is:

Inflation-adjusted income = $50,000 x (1 + 0.03)^30 = $121,363

Therefore, the best choice is A) $121,363.

Question 20

Dan plans to fund his individual retirement account (IRA)by contributing $2,000 at the end of each year for the next 10 years.If Dan can earn 10 percent on his contributions,how much will he have at the end of the tenth year?

Accepted Answer

Using the formula for future value of an annuity:

FV = (PMT x ((1+i)^n - 1)/i)

where PMT = payment (in this case, $2,000), i = interest rate per period (10% per year), and n = number of periods (10 years).

FV = (2000 x ((1+0.10)^10 - 1)/0.10)
FV = $31,875

Therefore, Dan will have $31,875 at the end of the tenth year.

Quiz 5: Time Value of Money

An annuity with an infinite life is called a(n) ________.