Question 1

The present value of a perpetuity:
A) conceptually doesn't make sense.
B) is infinite.
C) is zero.
D) is not affected by changes in the discount rate.
E) None of the above

Accepted Answer

The present value of a perpetuity is calculated as the payment amount divided by the discount rate. It is not infinite, zero, or unaffected by changes in the discount rate.

Question 2

Which of the following series of cash flows includes an imbedded annuity?
A) 10, 5, 6, 7, 8, 9, 10
B) 6, 6, 6, 6, 6, 6, 6
C) 5, 6, 7, 7, 7, 6, 7
D) 8, 7, 6, 5, 4, 3, 2
E) None of the above has an embedded annuity.

Accepted Answer

A series of cash flows that includes an embedded annuity is one where there is a fixed amount of cash flows occurring at regular intervals. In option C, the cash flows of 7 occur three times in a row, which is indicative of an imbedded annuity. The other options do not have a consistent flow of cash flows at regular intervals.

Question 3

A series of equal payments that occur at equal intervals and go on forever is called a(n):
A) ordinary annuity.
B) annuity due.
C) perpetuity.
D) non-ending stream.
E) None of the above

Accepted Answer

A perpetuity is a series of equal payments that occur at equal intervals and go on forever, unlike an ordinary annuity, which has a finite number of payments, or an annuity due, which has payments that occur at the beginning of each period instead of at the end. Therefore, the best choice is C, perpetuity.

Question 4

What is the most you should pay to receive the following cash flows if you require a return of 12 percent? $\begin{array}{ll}
\text { Year 1 } & \$ 5,000 \
\text { Year 2 } & \$ 8,000 \
\text { Year 3 } & \$ 12,000 \
\text { Year 4-10 } & \$ 15,000
\end{array}$
A) $58,580
B) $104,135
C) $68,105
D) None of the above

Accepted Answer

The answer of What is the most you should pay...

Question 5

$3,947 deposited four years ago has grown to $5,000. What semiannually compounded rate of interest has the bank been paying?
A) 5.26%
B) 6.00%
C) 3.00%
D) 6.67%

Accepted Answer

The answer of $3,947 deposited four years ago has grown...

Question 6

You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190. What was the annual rate of return on your investment?
A) 12%
B) 11%
C) 10%
D) 9%

Accepted Answer

The annual rate of return can be calculated using the formula for compound annual growth rate (CAGR), which is: $$CAGR = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$$ where $FV$ is the future value ($83,190), $PV$ is the present value ($30,000), and $n$ is the number of periods (9 years). Plugging in the values: $$CAGR = \left(\frac{83190}{30000}\right)^{\frac{1}{9}} - 1 \approx 0.12$$ or 12% annual rate of return.

Question 7

Designs Now is opening a showcase office to display and sell its computer designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows?
A) $429,720
B) $457,620
C) $456,000
D) $424,820

Accepted Answer

The answer of Designs Now is opening a showcase office...

Question 8

Determine how much $1,000 deposited in a savings account paying 8% compounded annually will be worth after 5 years.
A) $5,526
B) $784
C) $1,400
D) $1,469

Accepted Answer

To find the value after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the initial principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years. Plugging in the given values, we get:
A = 1000(1 + 0.08/1)^(1*5)
A = $1,469
Therefore, the answer is D.

Question 9

Using an annual interest rate of 9%, how long will it take a deposit of $1,000 to grow to $3,000, assuming no additional deposits are made?
A) 8.04 years
B) 10.00 years
C) 11.11 years
D) 12.75 years
E) 13.50 years

Accepted Answer

The answer of Using an annual interest rate of 9%,...

Question 10

Which of the following interest rates will come closest to doubling invested money in five years?
A) 13%
B) 14%
C) 15%
D) 16%

Accepted Answer

To calculate the number of years it takes for an investment to double, we use the "rule of 72." This rule is simply 72 divided by the interest rate. The result is the approximate number of years it takes for the investment to double.

Using this rule: 
For A) 72/13 = 5.5 years to double 
For B) 72/14 = 5.14 years to double 
For C) 72/15 = 4.8 years to double 
For D) 72/16 = 4.5 years to double

Therefore, among the given choices, the interest rate closest to doubling invested money in five years is C) 15%.

Question 11

At an effective interest rate of 12%, a single sum invested today will double itself in approximately:
A) 8 years.
B) 12 years.
C) 6 years.
D) insufficient data to determine answer.

Accepted Answer

Using the rule of 72, we can estimate how long it will take for an investment to double by dividing 72 by the annual interest rate. 
So, 72/12 = 6, which means the investment will double in approximately 6 years. Therefore, the best choice is C.

Question 12

What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two years later?
A) 12%
B) 25%
C) 6%
D) 18%
E) 4%

Accepted Answer

The rate of return can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and n is the time the money is invested for in years. Rearranging the formula to solve for r gives us r = [(A/P)^(1/n)] - 1. Substituting the given values (A = $1,254.70, P = $1,000, n = 2 years) gives us r = [(1254.70/1000)^(1/2)] - 1 = 0.12, or 12%.

Question 13

If a series of equal payments is paid regularly out of a bank account which earns a constant rate of interest, the ____ is the amount that must be in the bank at the beginning of the series to just fund all of the payments.
A) future value of an annuity due
B) present value of an annuity due
C) future value of an ordinary annuity
D) present value of an ordinary annuity
E) None of the above

Accepted Answer

The question is asking for the amount that must be in the bank at the beginning of the series, which is the present value of the payments. It is not an annuity due, so options A and B are incorrect. Additionally, since the payments are equal and are paid regularly, it is an ordinary annuity, making option C incorrect. The correct answer is therefore option D, the present value of an ordinary annuity.

Question 14

Your bank balance is exactly $10,000. Three years ago you deposited $7,938 and have not touched the account since. What annually compounded rate of interest has the bank been paying?
A) 8.65%
B) 26.00%
C) 8.00%
D) 6.87%

Accepted Answer

We can use the formula for compound interest: 
A=P(1+r/n)^(nt)
where 
A = final amount ($10,000 in this case)
P = principal deposit ($7,938)
r = annual interest rate (what we need to find)
n = number of times interest is compounded per year (not given)
t = time in years (3 years, since the deposit was made)

We can rewrite the formula as:
r = n[(A/P)^(1/nt) - 1]

First, we need to figure out the number of times interest is compounded per year. This information is not given in the problem, so we'll have to make a guess. Since banks typically compound interest either monthly or daily, we'll assume that the interest is compounded monthly. Therefore, n = 12.

Plugging in the numbers:
r = 12[(10,000/7,938)^(1/(12*3)) - 1]
r = 8.00%

Therefore, the bank has been paying an annual interest rate of 8.00%. The closest answer choice is C.

Question 15

If you invest the $10,000 you receive at graduation (age 22) in a mutual fund which averages a 12% annual return, how much will you have at retirement in 40 years?
A) $909,090
B) $930,510
C) $783,879
D) $510,285

Accepted Answer

Using the compound interest formula: 
A = P(1 + r/n)^(nt), where 
A = the final amount (what we want to solve for)
P = the principal amount (initial investment) = $10,000
r = annual interest rate as a decimal = 0.12
n = number of times interest is compounded per year = 1 (annually)
t = time (in years) = 40

Plugging in the values: 
A = 10,000(1 + 0.12/1)^(1*40)
A = $930,510.29

Therefore, the best choice is B, which is the closest to the calculated amount above.

Question 16

If a series of equal payments is received regularly at the end of the year, and each is deposited immediately at the same interest rate, the ____ is the sum of all the payments and all the interest earned at the end of the series.
A) future value of an annuity due
B) present value of an annuity due
C) future value of an ordinary annuity
D) present value of an ordinary annuity
E) none of the above

Accepted Answer

The scenario described is that of a future value of an ordinary annuity, where payments are made at the end of each period (in this case, at the end of each year) and interest is earned on those payments. The formula for calculating the future value of an ordinary annuity takes into account both the sum of the payments and the interest earned on them.

Question 17

Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident. What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%.
A) $153,900
B) $68,100
C) $65,000
D) $70,800

Accepted Answer

The answer of Five years after an accident, you received...

Question 18

How much must be invested today to have $1,000 in two years if the interest rate is 5%?
A) $909.09
B) $900.00
C) $907.00
D) $950.00

Accepted Answer

The answer of How much must be invested today to...

Question 19

A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever).
A) imbedded annuity
B) annuity due
C) sinking fund
D) perpetuity

Accepted Answer

A perpetuity is a financial instrument that pays an equal amount of money per period indefinitely, making it a type of infinite annuity. The other options are not perpetuities. An embedded annuity is a feature within another financial instrument, such as a bond, that includes regular payments to the holder. An annuity due is a financial instrument that requires payments to be made at the beginning of each period rather than at the end. A sinking fund is a fund established by an organization to set aside money to pay off a debt or other obligation.

Question 20

Find the present value of $100 to be received at the end of two years if the discount rate is 12% compounded monthly.
A) $66.50
B) $78.76
C) $68.80
D) $91.80
E) $79.75

Accepted Answer

The answer of Find the present value of $100 to...

Quiz 6: Time Value of Money

The present value of a perpetuity:

Which of the following series of cash flows includes an imbedded annuity?

A series of equal payments that occur at equal intervals and go on forever is called a(n) :

What is the most you should pay to receive the following cash flows if you require a return of 12 percent? $\begin{array}{ll}\text { Year 1 } & \$ 5,000 \\\text { Year 2 } & \$ 8,000 \\\text { Year 3 } & \$ 12,000 \\\text { Year 4-10 } & \$ 15,000\end{array}$

$3,947 deposited four years ago has grown to $5,000. What semiannually compounded rate of interest has the bank been paying?

You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190. What was the annual rate of return on your investment?

Determine how much $1,000 deposited in a savings account paying 8% compounded annually will be worth after 5 years.

Using an annual interest rate of 9%, how long will it take a deposit of $1,000 to grow to $3,000, assuming no additional deposits are made?

Which of the following interest rates will come closest to doubling invested money in five years?

At an effective interest rate of 12%, a single sum invested today will double itself in approximately:

What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two years later?

If a series of equal payments is paid regularly out of a bank account which earns a constant rate of interest, the ____ is the amount that must be in the bank at the beginning of the series to just fund all of the payments.

Your bank balance is exactly $10,000. Three years ago you deposited $7,938 and have not touched the account since. What annually compounded rate of interest has the bank been paying?

If you invest the $10,000 you receive at graduation (age 22) in a mutual fund which averages a 12% annual return, how much will you have at retirement in 40 years?

If a series of equal payments is received regularly at the end of the year, and each is deposited immediately at the same interest rate, the ____ is the sum of all the payments and all the interest earned at the end of the series.

Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident. What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%.

How much must be invested today to have $1,000 in two years if the interest rate is 5%?

A(n) ____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever) .

Find the present value of $100 to be received at the end of two years if the discount rate is 12% compounded monthly.