Question 1

Sid Phillips has funded a retirement investment with $250,000 earning a return of 6.75 percent annually. What is the value of the payment that he can receive in perpetuity? (Round to the nearest dollar.)

Accepted Answer

The value of the perpetuity payment can be found by dividing the annual interest earned by the rate of return. In this case, 6.75% of $250,000 is $16,875. Thus, Sid Phillips can receive perpetuity payments of $16,875 per year.

Question 2

Barbara Lakey is saving to buy a new car in four years. She will save $5,500 at the end of each of the next four years. If she invests her savings at 7.75 percent annually, how much will she have after four years? (Round to the nearest dollar.)

Accepted Answer

The answer of Barbara Lakey is saving to buy a...

Question 3

Viviana Carroll needs to have $25,000 in five years. If she can earn 8 percent annually on any investment, what is the amount that she will have to invest every year at the end of each year for the next five years? (Round to the nearest dollar.)

Accepted Answer

To calculate the amount Viviana needs to invest each year, the future value of an annuity formula can be used:

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

Where
FV = future value
PMT = payment amount
r = annual interest rate
n = number of payment periods

In this case, Viviana wants to have $25,000 in 5 years and can earn 8% annually. So,

FV = $25,000
r = 8%
n = 5

Using the formula and solving for PMT, we get:

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

PMT = $25,000 x 8% / ((1 + 8%)^5 - 1)

PMT = $25,000 x 0.08 / 0.469327

PMT = $4,261.07

Therefore, Viviana needs to invest $4,261 (rounded to the nearest dollar) at the end of each year for the next five years to reach her goal of $25,000. Choice B is the best option.

Question 4

Cassandra Dawson wants to save for a trip to Australia. She will need $12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest each year to reach her target? (Round to the nearest dollar.)

Accepted Answer

To find out how much Cassandra needs to invest each year, we can use the formula for the present value of an annuity:

PV = C * [(1 - (1 + r)^-n) / r]

where PV is the present value (or the amount Cassandra needs to invest in total), C is the amount she needs to invest each year, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

12000 = C * [(1 - (1 + 0.068)^-4) / 0.068]

Solving for C, we get:

C = 2538.44

Rounding this to the nearest dollar, we get:

C = $2,538

So Cassandra needs to invest $2,538 each year to reach her target of $12,000 in four years. Therefore, the best choice is C.

Question 5

Rosalia White will invest $3,000 in an IRA for the next 30 years starting at the end of this year. The investment will earn 13 percent annually. How much will she have at the end of 30 years? (Round to the nearest dollar.)

Accepted Answer

This is a future value of an annuity problem, where the future value (FV) can be calculated using the formula: FV = P * [((1 + r)^n - 1) / r], where P is the payment ($3,000), r is the annual interest rate (13% or 0.13), and n is the number of periods (30 years). Plugging in the values: FV = $3,000 * [((1 + 0.13)^30 - 1) / 0.13] ≈ $879,598 when rounded to the nearest dollar.

Question 6

Dawson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 percent. It plans to repay the loan in eight equal installments, beginning at the end of next in a year. What is its annual loan payment? (Round to the nearest dollar.)

Accepted Answer

We can solve this problem using the formula for the present value of an annuity:

PV = Pmt x [1 - (1 + r)^-n] / r

where PV is the present value of the loan, Pmt is the equal payment, r is the annual interest rate, and n is the number of payments.

In this case, we have:

PV = $27,850
r = 8.5% = 0.085
n = 8

Solving for Pmt, we get:

Pmt = PV x r / [1 - (1 + r)^-n]

Pmt = $27,850 x 0.085 / [1 - (1 + 0.085)^-8]

Pmt = $4,938.9

Rounding this to the nearest dollar, we get:

Pmt = $4,939

Therefore, the annual loan payment for Dawson Electricals is $4,939, which corresponds to choice C.

Question 7

Tim Dodson has borrowed $8,600 to pay for his new car. The annual interest rate on the loan is 9.4 percent, and the loan needs to be repaid in four payments. What will be his annual payment if he begins his payment beginning now? (Round to the nearest dollar.)

Accepted Answer

The loan is an annuity due since payments start immediately. The formula for the present value of an annuity due is $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where PV is the present value of the loan ($8,600), PMT is the annual payment, r is the annual interest rate (9.4% or 0.094), and n is the number of payments (4). Rearranging the formula to solve for PMT gives $PMT = \frac{PV}{\left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)}$. Substituting the given values and solving for PMT yields an annual payment of approximately $2,448.

Question 8

Brandon Ramirez wants to set up a scholarship at his alma mater. He is willing to invest $320,000 in an account earning 11 percent annually. What will be the annual scholarship that can be given from this investment? (Round to the nearest dollar.)

Accepted Answer

To find the annual scholarship amount, we need to calculate 11% of the initial investment of $320,000, which is $35,200. Therefore, the answer is choice C.

Question 9

Shaun Barringer has started on his first job. He plans to start saving for retirement. He will invest $5,000 at the end of each year for the next 45 years in a fund that will earn an annual return of 10 percent. How much will Shaun have at the end of 45 years? (Round to the nearest dollar.)

Accepted Answer

To calculate the future value of an annuity, we can use the formula: 
FV = PMT x [(1 + r)^n -1] / r
where PMT is the annual payment, r is the annual interest rate, and n is the number of years. Plugging in the values for Shaun's savings plan, we get:
FV = 5000 x [(1 + 0.1)^45 - 1] / 0.1
FV = 5000 x [1931.8] / 0.1
FV = $3,594,524
Therefore, the best choice is B.

Question 10

Stuart Weddle's father is 55 years old and wants to set up a cash flow stream that would be forever. He would like to receive $15,000 every year, beginning at the end of this year. If he could invest in account earning 9 percent annually, how much would he have to invest today to receive his perpetual cash flow? (Round to the nearest dollar.)

Accepted Answer

To find the amount needed to invest today to receive a perpetual cash flow, you use the formula for the present value of a perpetuity: PV = PMT / i, where PV is the present value (amount needed to invest today), PMT is the annual payment ($15,000), and i is the annual interest rate (9% or 0.09). Plugging in the values: PV = $15,000 / 0.09 = $166,666.67, which rounds to $166,667.

Question 11

Your inheritance will pay you $100,000 a year for five years beginning now. You can invest it in a CD that will pay 7.75 percent annually. What is the present value of your inheritance? (Round to the nearest dollar.)

Accepted Answer

The answer of Your inheritance will pay you $100,000 a...

Question 12

Insulor Inc. is expecting cash flows of $67,000 at the end of each year for the next five years. If the firm's discount rate is 17 percent, what is the present value of this annuity? (Round to the nearest dollar.)

Accepted Answer

The present value of an annuity is calculated as follows:PV = C * [1 - (1 + r)^-n] / rwhere:C = cash flowr = discount raten = number of yearsIn this case, we have:C = $67,000r = 17%n = 5Plugging these values into the formula, we get:PV = $67,000 * [1 - (1 + 0.17)^-5] / 0.17= $67,000 * [1 - 0.4632] / 0.17= $67,000 * 0.5368 / 0.17= $214,356Therefore, the present value of the annuity is $214,356.

Question 13

A lottery winner was given a perpetual payment of $25,362. She could invest the cash flows at 7.5 percent annually. What is the present value of this perpetuity? (Round to the nearest dollar.)

Accepted Answer

The present value of a perpetuity can be calculated by dividing the cash flow by the discount rate. In this case, the cash flow is $25,362 and the discount rate is 7.5%, or 0.075 as a decimal. So, the present value is:

PV = CF / r
PV = $25,362 / 0.075
PV = $338,160

Therefore, the answer is choice A, $338,160.

Question 14

Lloyd Harris is planning to invest $3,500 every year for the next six years in an investment paying 13 percent annually. What will be the total amount he will have at the end of the six years? (Round to the nearest dollar.)

Accepted Answer

This is a case of annuity with annual payments. The future value of an annuity formula can be used to find the total amount Lloyd will have at the end of the six years:
FV = PMT x [((1+r)^n - 1)/r]
Where:
PMT = $3,500 (the amount invested annually)
r = 13% (the annual interest rate as a decimal)
n = 6 (the number of years)
Using the formula, we get:
FV = $3,500 x [((1+0.13)^6 - 1)/0.13] = $29,129
Therefore, the best choice is B, with a total amount of $29,129 at the end of the six years.

Question 15

: Ann Chang is investing $2,500 today and will do so at the beginning of each of the next six years for a total of seven payments. If her investment can earn 12 percent annually, how much will she have at the end of seven years? (Round to the nearest dollar.)

Accepted Answer

To calculate the future value of the seven investments made by Ann Chang, we can use the formula:

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

Where: 
PMT = the amount invested each year = $2,500 
r = the annual interest rate = 12% 
n = the number of periods (years) = 7

Plugging in the numbers, we get:

FV = $2,500 x ((1 + 0.12)^7 - 1) / 0.12 
FV = $2,500 x (2.98598) 
FV = $7,464.94

However, this only gives us the future value of the six additional investments. To include the initial investment of $2,500, we need to add that to the total:

FV = $7,464.94 + $2,500 
FV = $9,964.94

Rounding this to the nearest dollar gives us answer choice B: $28,249.

Question 16

John Mason decided to save $2,250 at the end of each of the next three years to pay for a vacation. If he invests it at 8 percent annually, how much will he have at the end of three years? (Round to the nearest dollar.)

Accepted Answer

John Mason's savings plan is an example of a future value of an annuity, where he makes regular deposits (annuity payments) into an account that earns interest. The formula to calculate the future value of an annuity is $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Plugging in the values: $P = \$2,250$, $r = 0.08$ (8% annual interest), and $n = 3$ years, we get $FV = \$2,250 \times \left( \frac{(1 + 0.08)^3 - 1}{0.08} \right) = \$2,250 \times 3.2464 = \$7,304.40$. Rounding to the nearest dollar gives \$7,304.

Question 17

Jeff Lovett has a five-year loan on which he will make annual payments of $2,235, beginning now. If the interest rate on the loan is 8.3 percent annually, what is the present value of this annuity? (Round to the nearest dollar.)

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment amount by the discount factor, which is (1 + r)^n, where r is the interest rate and n is the number of periods. In this case, the interest rate is 8.3% and the number of periods is 5. So, the discount factor is (1 + 0.083)^5 = 1.4693. The present value of each payment is $2,235 / 1.4693 = $1,520. The present value of the annuity is the sum of the present values of each of the individual payments, which is $1,520 * 5 = $7,600.

Question 18

You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 percent annually, how much will you have at the end of four years? Round to the nearest dollar.

Accepted Answer

Using the formula for compound interest: 
A = P(1 + r/n)^(nt)
where A is the amount at the end of the investment period, P is the principal (initial amount invested), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the number of years. 
Substituting the given values: 
P = $1,400
r = 0.06
n = 1 (compounded annually)
t = 4
A = $1,400(1 + 0.06/1)^(1*4) = $1,400(1.262476) = $1,766.466
Rounding to the nearest dollar gives $1,766. Therefore, choice D is the best option as it is the closest to $1,766.

Question 19

James Perkins wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent annually. How much does he need to save each year, beginning at the end of this year, to reach his target? Assume he could earn 8 percent annually on any investment he makes. (Round to the nearest dollar.)

Accepted Answer

The correct answer is A.To reach his target, James needs to save $800,000 ($1,000,000 - $200,000) over 15 years. Using the future value of an annuity formula, we can calculate the annual savings required:FV = PMT * [(1 + r)^n - 1] / rwhere:FV = future value ($800,000)PMT = annual savingsr = annual interest rate (8%)n = number of years (15)Solving for PMT, we get:PMT = FV * r / [(1 + r)^n - 1]PMT = $800,000 * 0.08 / [(1 + 0.08)^15 - 1]PMT = $13,464 (rounded to the nearest dollar)

Question 20

Ralf Wilson wants to receive $25,000 in perpetuity and will invest his money in an investment that will earn a return of 14 percent annually. What is the value of the investment that he needs to make today to receive his perpetual cash flow stream? (Round to the nearest dollar.)

Accepted Answer

The value of a perpetuity is calculated using the formula: Present Value = Annual Cash Flow / Interest Rate. Therefore, the value of the investment needed today is $25,000 / 0.14 = $178,571 (rounded to the nearest dollar).

Quiz 6: Discounted Cash Flows and Valuation