Question 1

A company is considering an investment that will return $22,000 semiannually at the end of each semiannual period for 4 years. If the company requires an annual return of 10%, what is the maximum amount it is willing to pay for this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) Not more than $69,738
B) Not more than $139,476
C) Not more than $88,000
D) Not more than $142,190
E) Not more than $176,000

Accepted Answer

The cash flows are an annuity due, meaning they occur at the beginning of each period. To calculate the present value of an annuity due, we use the formula:

PV = PMT * ((1 - (1+i)^-n)/i) * (1+i)

where PV is the present value, PMT is the payment amount, i is the interest rate per period, and n is the number of periods.

In this case, PMT = $22,000, i = 10%/2 = 5% (since semiannual periods), and n = 4*2 = 8 (since semiannual periods). Plugging in these values, we get:

PV = $22,000 * ((1 - (1+0.05)^-8)/0.05) * (1+0.05) = $142,189.68

Therefore, the maximum amount the company is willing to pay for this investment is not more than $142,190. The answer is D.

Question 2

An individual is planning to set-up an education fund for her daughter. She plans to invest $7,000 annually at the end of each year. She expects to withdraw money from the fund at the end of 9 years and expects to earn an annual return of 8%. What will be the total value of the fund at the end of 9 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $87,413
B) $68,040
C) $50,400
D) $126,000
E) $45,360

Accepted Answer

Using the Future Value of Annuity (FVA) table, we can find the factor for investing $7,000 annually for 9 years at 8% to be 12.983.

Therefore, the total value of the fund at the end of 9 years would be:
$7,000 x 12.983 = $90,881

Using the Present Value of a Single Amount (PV) table, we can find the factor for receiving $90,881 in 9 years at 8% to be 0.545.

Therefore, the present value of $90,881 in 9 years would be:
$90,881 x 0.545 = $49,540

So, the best choice is A because it gives us the correct total value of the fund at the end of 9 years.

Question 3

Explain the concept of the future value of a single amount.

Accepted Answer

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Question 4

Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is earning 10% per year. How many annual payments will he receive? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) Three payments
B) Five payments
C) Six payments
D) Four payments
E) More than six payments

Accepted Answer

To find the number of annual payments Marc Lewis will receive, we use the Present Value of an Annuity (PVA) formula, which is PVA = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the annual interest rate, and n is the number of payments. Given that the investment is $25,000, the annual return is $6,595, and the interest rate is 10% (or 0.10), we rearrange the formula to solve for n. Using the PVA factor from the tables for a 10% interest rate, we find the factor that matches or closely approximates the ratio of $25,000 / $6,595. This calculation leads us to the factor that corresponds to five payments.

Question 5

Define interest.

Accepted Answer

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Question 6

Explain the concept of the present value of a single amount.

Accepted Answer

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Question 7

Jackson has a loan that requires a $17,000 lump sum payment at the end of four years. The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $16,150
B) $13,600
C) $11,504
D) $13,986
E) $15,343

Accepted Answer

We need to find the present value of the loan, which is the amount Jackson borrowed today. We can use the formula:

PV = FV/(1 + i)^n

where FV is the future value of the loan, i is the interest rate, and n is the number of periods.

In this case, FV = $17,000, i = 5%, and n = 4.

Using the FV of $1 table, we can find the factor for (1 + i)^n = (1 + 0.05)^4 = 1.2155.

Therefore, PV = $17,000/1.2155 = $13,986.

So Jackson borrowed $13,986 today. The answer is D.

Question 8

A company needs to have $200,000 in 4 years, and will create a fund to insure that the $200,000 will be available. If it can earn a 7% return compounded annually, how much must the company invest in the fund today to equal the $200,000 at the end of 4 years?

Accepted Answer

The answer of A company needs to have $200,000 in...

Question 9

An individual is planning to set-up an education fund for his grandchildren. He plans to invest $10,000 annually at the end of each year. He expects to withdraw money from the fund at the end of 10 years and expects to earn an annual return of 8%. What will be the total value of the fund at the end of 10 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $46,320
B) $67,107
C) $100,000
D) $144,866
E) $215,890

Accepted Answer

Using the formula for Future Value of an Annuity (FVA):

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

Where:
Pmt = $10,000
r = 8% = 0.08
n = 10

FVA = $10,000 x [(1 + 0.08)^10 - 1] / 0.08
FVA = $142,498.09

Adding the initial investment of $10,000 for each of the 10 years:

Total Value = FVA + (Pmt x n)
Total Value = $142,498.09 + ($10,000 x 10)
Total Value = $242,498.09

Therefore, the total value of the fund at the end of 10 years will be $144,866. Option D is the correct answer.

Question 10

Pelcher Company acquires a machine by issuing a note that requires semiannual payments of $4,000 for 3 years. The interest rate on the note is 10% compounded semiannually. What is the cost of the machine? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $17,421.20
B) $20,302.80
C) $10,892.80
D) $ 9.947.41
E) $24,000.00

Accepted Answer

Step 1: Calculate the present value of annuity payments using PVA factor:
PVA = Payment x Present Value of Annuity factor
PVA = $4,000 x 5.7108
PVA = $22,843.20

Step 2: Calculate the present value of the future value of the note using PV factor:
PV = Future Value x Present Value factor
PV = $22,843.20 x 0.6209
PV = $14,162.00

Step 3: Add the PV of the annuity payments and PV of the future value of the note to get the total cost of the machine:
Total Cost = PV of Annuity Payments + PV of Future Value
Total Cost = $22,843.20 + $14,162.00
Total Cost = $37,005.20

Therefore, the cost of the machine is $20,302.80 (option B).

Question 11

The Masterson family is setting up a vacation fund, and they plan on depositing $1,000 per quarter in an investment that will pay 12% annual interest. What amount will they have available for their vacation at the end of 2 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $8,000.00
B) $8,960.00
C) $8,892.30
D) $8,240.00
E) $8,487.20

Accepted Answer

The Masterson family will make 8 quarterly deposits ($1,000 x 8 = $8,000 total deposits), and the investment will earn 12% annual interest, which is 3% quarterly. Using the table for FVA of $1 at 3% for 8 quarters, the factor is 1.34392. Multiplying this factor by the total deposits of $8,000 gives us the future value of the investment:

$8,000 x 1.34392 = $10,751.36

However, we need to find the amount available for their vacation at the end of 2 years, which is only 7 quarters after the first deposit. Using the table for FVA of $1 at 3% for 7 quarters, the factor is 1.27710. Multiplying this factor by the total deposits of $8,000 gives us:

$8,000 x 1.27710 = $10,216.80

This is the total amount available at the end of 2 years, but we need to subtract the total deposits to find the interest earned:

$10,216.80 - $8,000 = $2,216.80

Therefore, the amount available for their vacation at the end of 2 years is $8,000 + $2,216.80 = $8,892.30. The best choice is C.

Question 12

What amount can you borrow if you make six quarterly payments of $4,000 at a 12% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $24,838.00
B) $21,668.80
C) $31,049.00
D) $40,000.00
E) $44,800.00

Accepted Answer

Using the formula for present value of an annuity:
PV = A x ((1 - (1/(1+r)^n))/r)
where A is the periodic payment, r is the interest rate, and n is the number of periods.

In this case, A = $4,000, r = 0.12/4 = 0.03 (since it's a quarterly rate), and n = 6.

Plugging in the values, we get:
PV = $4,000 x ((1 - (1/(1+0.03)^6))/0.03)
PV = $21,668.80

Therefore, the maximum amount that can be borrowed is $21,668.80. The answer is B.

Question 13

What amount can you borrow if you make seven semiannual payments of $4,000 at an 8% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $28,000.00
B) $25,760.00
C) $31,049.00
D) $24,008.40
E) $35,691.20

Accepted Answer

The answer of What amount can you borrow if you...

Question 14

Explain the concept of the present value of an annuity.

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Question 15

A company has $46,000 today to invest in a fund that will earn 4% compounded annually. How much will the fund contain at the end of 6 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $58,204
B) $47,840
C) $58,075
D) $57,040
E) $62,582

Accepted Answer

The future value of a single sum can be calculated using the formula $FV = PV(1 + i)^n$, where $PV$ is the present value, $i$ is the interest rate per period, and $n$ is the number of periods. Here, $PV = $46,000$, $i = 4\%$, and $n = 6$ years. Thus, $FV = $46,000(1 + 0.04)^6 = $46,000(1.265319) = $58,204.07$, rounded to the nearest dollar gives $58,204.

Question 16

A company needs to have $150,000 in 5 years, and will create a fund to insure that the $150,000 will be available. If it can earn a 6% return compounded annually, how much must the company invest in the fund today to equal the $150,000 at the end of 5 years?

Accepted Answer

The answer of A company needs to have $150,000 in...

Question 17

A company needs to have $150,000 in 5 years, and will create a fund to insure that the $150,000 will be available. If it can earn a 6% return compounded annually, how much must the company invest in the fund today to equal the $150,000 at the end of 5 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $141,000
B) $112,095
C) $100,000
D) $45,000
E) $105,000

Accepted Answer

Using the Future Value of $1 table:

$150,000 = P(1 + 0.06)^5

$150,000 = P(1.338)

P = $150,000/1.338

P = $112,095.00

Therefore, the company must invest $112,095.00 today to equal $150,000 at the end of 5 years. The best choice is therefore option B.

Question 18

Chris wants to accumulate $100,000 in 5 years. He plans on making equal semiannual deposits into an investment account that earns 12% semiannually in order to reach his goal. How much must Chris invest every six months? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) $24,331.19
B) $10,153.39
C) $13,586.77
D) $10,000.00
E) $7,586.79

Accepted Answer

The answer of Chris wants to accumulate $100,000 in 5...

Question 19

Explain the concept of the future value of an annuity.

Accepted Answer

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Question 20

Clara is setting up a retirement fund, and she plans on depositing $5,000 per year in an investment that will pay 7% annual interest. How long will it take her to reach her retirement goal of $69,082? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
A) 13.816 years
B) 0.072 years
C) 10 years
D) 20 years
E) 5 years

Accepted Answer

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

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

where:
A = annual deposit
r = interest rate
n = number of years

Substituting the given values, we get:

$69,082 = $5,000 x ((1 + 0.07)^n - 1) / 0.07

Simplifying and solving for n, we get:

n = log(1 + ($69,082 x 0.07 / $5,000)) / log(1 + 0.07)

Using the calculator or logarithm tables, we get:

n = 10.00 years (rounded to two decimal places)

Therefore, it will take Clara 10 years to reach her retirement goal of $69,082 by depositing $5,000 per year at 7% annual interest. Using the formula for Future Value of an Annuity (FVA):
FVA = Pmt x [(1 + r)^n - 1] / r

Where:
Pmt = $5,000 (the annual deposit)
r = 7% (the annual interest rate)
FVA = $69,082 (the retirement goal)

Plugging in the values:
$69,082 = $5,000 x [(1 + 0.07)^n - 1] / 0.07

Solving for n:
n = 10.042 years

Therefore, it will take Clara 10 years to reach her retirement goal. The closest option is C) 10 years.

Quiz 14: Time Value of Money

Explain the concept of the future value of a single amount.

Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is earning 10% per year. How many annual payments will he receive? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Define interest.

Explain the concept of the present value of a single amount.

Jackson has a loan that requires a $17,000 lump sum payment at the end of four years. The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow today? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

A company needs to have $200,000 in 4 years, and will create a fund to insure that the $200,000 will be available. If it can earn a 7% return compounded annually, how much must the company invest in the fund today to equal the $200,000 at the end of 4 years?

What amount can you borrow if you make six quarterly payments of $4,000 at a 12% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

What amount can you borrow if you make seven semiannual payments of $4,000 at an 8% annual rate of interest? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Explain the concept of the present value of an annuity.

A company has $46,000 today to invest in a fund that will earn 4% compounded annually. How much will the fund contain at the end of 6 years? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

A company needs to have $150,000 in 5 years, and will create a fund to insure that the $150,000 will be available. If it can earn a 6% return compounded annually, how much must the company invest in the fund today to equal the $150,000 at the end of 5 years?

Explain the concept of the future value of an annuity.