Question 1

If Sloane Joyner invests $10,514.81 now and she will receive $30,000 at the end of 11 years, what annual rate of interest will she be earning on her investment?
A)8%
B)8.5%
C)9%
D)10%

Accepted Answer

The answer of If Sloane Joyner invests $10,514.81 now and...

Question 2

Suppose you have a winning lottery ticket and you are given the option of accepting $3,000,000 three years from now or taking the present value of the $5,000,000 now.The sponsor of the prize uses a 6% discount rate.If you elect to receive the present value of the prize now, the amount you will receive is
A)$2,518,860.
B)$2,591,520.
C)$2,670,000.
D)$3,000,000.

Accepted Answer

The present value of the prize can be calculated using the formula:PV = FV / (1 + r)^nwhere:PV is the present valueFV is the future valuer is the discount raten is the number of yearsIn this case, the future value is $5,000,000, the discount rate is 6%, and the number of years is 3. Plugging these values into the formula, we get:PV = $5,000,000 / (1 + 0.06)^3 = $2,518,860Therefore, the amount you will receive if you elect to receive the present value of the prize now is $2,518,860.

Question 3

Dexter Company is considering purchasing equipment.The equipment will produce the following cash flows: $\begin{array}{ll}
\text { Year 1 } & \$ 120,000 \
\text { Year 2 } & \$ 200,000
\end{array}$ Dexter requires a minimum rate of return of 10%.What is the maximum price Dexter should pay for this equipment?
A)$274,380
B)$165,290
C)$320,000
D)$160,000

Accepted Answer

The maximum price Dexter should pay is the present value of the cash flows discounted at the required rate of return (10%). The present value of Year 1 is $ \$120,000 / (1+0.10)^1 = \$109,090.91 $ and Year 2 is $ \$200,000 / (1+0.10)^2 = \$165,289.26 $. The total present value is approximately \$274,380.

Question 4

Perdue Company has purchased equipment that requires annual payments of $30,000 to be paid at the end of each of the next 6 years.The appropriate discount rate is 12%.What amount will be used to record the equipment?
A)$180,000
B)$123,342
C)$165,772
D)$115,650

Accepted Answer

The present value of an annuity due formula is used to calculate the present value of the equipment payments. Using a financial calculator or spreadsheet program, the present value of the payments is $123,342. This is the amount that should be recorded as the purchase cost of the equipment. Therefore, the correct answer is B.

Question 5

In present value calculations, the process of determining the present value is called
A)allocating.
B)pricing.
C)negotiating.
D)discounting.

Accepted Answer

The process of determining the present value is called discounting. It involves reducing future cash flows to their present value by applying a discount rate that reflects the time value of money. This means that cash flows expected to be received in the future are worth less than cash flows received today, because of the potential for earning interest on the money over time. Therefore, discounting is the most appropriate choice for this question.

Question 6

Hazel Company has just purchased equipment that requires annual payments of $40,000 to be paid at the end of each of the next 4 years.The appropriate discount rate is 15%.What is the present value of the payments?
A)$114,199
B)$160,000
C)$46,975
D)$150,135

Accepted Answer

The present value of an annuity can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the discount rate, and n is the number of periods. Plugging in the given values (PMT = $40,000, r = 0.15, n = 4), the calculation gives a present value of approximately $114,199.

Question 7

Present value is based on
A)the dollar amount to be received.
B)the length of time until the amount is received.
C)the interest rate.
D)all of these.

Accepted Answer

Present value is determined by the dollar amount to be received, the length of time until it is received, and the interest rate, as all these factors affect the discounting process.

Question 8

The amount you must deposit now in your savings account, paying 6% interest, in order to accumulate $6,000 for a down payment 5 years from now on a new car is
A)$1,200.
B)$4,484.
C)$4,477.
D)$4,200.

Accepted Answer

To find the present value (the amount you must deposit now) to accumulate a future sum, you use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($6000), r is the interest rate per period (6% or 0.06), and n is the number of periods (5 years). Plugging in the values: PV = $6000 / (1 + 0.06)^5 ≈ $4484.

Question 9

A $10,000, 6%, 5-year note payable that pays interest quarterly would be discounted back to its present value by using tables that would indicate which one of the following period-interest combinations?
A)5 interest periods, 6% interest
B)20 interest periods, 6% interest
C)20 interest periods, 1.5% interest
D)5 interest periods, 1.5% interest

Accepted Answer

We need to find the present value of a $10000 6% 5-year note payable that pays interest quarterly. Therefore, we need to use tables that show the periodic interest for quarterly payments. That is, we need the interest rate per quarter. The formula to calculate this interest rate is:

(1 + periodic interest rate)^number of periods = 1 + annual interest rate
(1 + i)^4 = 1 + 0.06
(1 + i) = (1 + 0.06)^(1/4)
(1 + i) = 1.01477
i = 0.01477 or 1.477%

Therefore, we need to use tables that indicate 20 interest periods (5 years * 4 quarters per year) at a periodic interest rate of 1.5% (half of the quarterly interest rate we just calculated). Choice C is the only option that meets these criteria.

Question 10

The present value of $10,000 to be received in 5 years will be smaller if the discount rate is
A)increased.
B)decreased.
C)not changed.
D)equal to the stated rate of interest.

Accepted Answer

The present value of a future amount decreases as the discount rate increases. Therefore, if the discount rate is increased, the present value of $10,000 to be received in 5 years will be smaller.

Question 11

If the single amount of $3,000 is to be received in 3 years and discounted at 6%, its present value is
A)$2,519.
B)$2,830.
C)$2,600.
D)$2,820.

Accepted Answer

Using the formula for present value of a single amount: 
PV = FV / (1 + r)^n
where PV is present value, FV is future value, r is the interest rate, and n is the number of years.

Plugging in the values given:
PV = 3,000 / (1 + 0.06)^3 = $2,519.

Question 12

Which of the following discount rates will produce the smallest present value?
A)8%
B)9%
C)10%
D)4%

Accepted Answer

The higher the discount rate, the lower the present value. Therefore, a discount rate of 10% will produce the smallest present value among the options given.

Question 13

If you are able to earn an 8% rate of return, what amount would you need to invest to have $30,000 one year from now?
A)$27,747
B)$27,778
C)$27,273
D)$29,700

Accepted Answer

We can use the formula FV = PV(1+r), where FV is the future value, PV is the present value, and r is the interest rate expressed as a decimal. Plugging in the given values, we get:

30,000 = PV(1+0.08)
PV = 27,777.78

Rounding to the nearest dollar, the answer is B) $27,778.

Question 14

The amount you must deposit now in your savings account, paying 5% interest, in order to accumulate $10,000 for your first tuition payment when you start college in 3 years is
A)$8,500.
B)$7,830.
C)$8,638.
D)$8,860.

Accepted Answer

We can use the formula for present value of a future payment, which is given by:

$PV = \frac{FV}{(1+r)^n}$

Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.

In this case, we know FV = $10,000$, r = $0.05$, and n = 3. We want to solve for PV.

$PV = \frac{10,000}{(1+0.05)^3} \approx 8,638$

Therefore, the amount you must deposit now is approximately $8,638. Option C is the closest to this value.

Question 15

Peter Johnson invests $35,516.80 now for a series of $5,000 annual returns beginning one year from now.Peter will earn 10% on the initial investment.How many annual payments will Peter receive?
A)10
B)12
C)13
D)15

Accepted Answer

The present value of the investment is $35,516.80 and Peter will earn 10% annually. Using the formula for the present value of an annuity, we can calculate the number of annual payments Peter will receive:
PV = PMT x (1 - 1/(1+r)^n) / r
Where PV is the present value, PMT is the payment, r is the interest rate, and n is the number of payments.
Plugging in the values, we get:
35,516.80 = 5,000 x (1 - 1/(1+0.1)^n) / 0.1
Simplifying, we get:
7.10336 = (1 - 1.1^-n)
Taking the natural logarithm of both sides, we get:
ln(7.10336) = ln(1 - 1.1^-n)
Solving for n, we get:
n = - ln(1 - ln(7.10336)) / ln(1.1)
n ≈ 12.72
Since Peter can't receive a partial payment, he will receive 13 annual payments. Therefore, the answer is C.

Question 16

Suzy Douglas has been offered the opportunity of investing $73,540 now.The investment will earn 8% per year and at the end of its life will return $200,000 to Suzy.How many years must Suzy wait to receive the $200,000?
A)10
B)11
C)12
D)13

Accepted Answer

To find the number of years Suzy must wait to receive $200,000, we can use the formula for the future value of a single sum, which is $FV = PV(1 + r)^n$, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Rearranging the formula to solve for n gives us $n = \frac{\log(FV/PV)}{\log(1 + r)}$.Plugging in the values from the question:- $FV = $200,000$- $PV = $73,540$- $r = 8\% = 0.08$We get $n = \frac{\log(200000/73540)}{\log(1.08)}$.Calculating this gives us approximately 13 years.

Question 17

Which of the following accounting problems does not involve a present value calculation?
A)The determination of the market price of a bond.
B)The determination of the declining-balance depreciation expense.
C)The determination of the amount to report for long-term notes payable.
D)The determination of the amount to report for lease liability.

Accepted Answer

The determination of declining-balance depreciation expense is a method of calculating depreciation expense based on a fixed rate applied to the declining book value of an asset each year. It does not involve a present value calculation. The other options (A, C, and D) all require present value calculations to determine the market price of a bond, the amount to report for long-term notes payable, and the amount to report for lease liability, respectively.

Question 18

If you are able to earn a 15% rate of return, what amount would you need to invest to have $15,000 one year from now?
A)$14,852
B)$13,125
C)$12,750
D)$13,044

Accepted Answer

We can use the formula:
FV = PV x (1 + r)
where FV is the future value, PV is the present value (the amount we need to invest), r is the rate of return as a decimal.
Plugging in the numbers we know, we get:
$15,000 = PV x (1 + 0.15)
Simplifying, we get:
$15,000 = PV x 1.15
Dividing both sides by 1.15, we get:
PV = $13,043.48, which is closest to answer D, $13,044.

Question 19

If the single amount of $2,000 is to be received in 2 years and discounted at 11%, its present value is
A)$1,818.
B)$1,623.
C)$1,802.
D)$2,754.

Accepted Answer

Using the present value formula: 
PV = FV / (1+r)^n
PV = 2,000 / (1+0.11)^2
PV = 2,000 / 1.2544
PV = $1,623.

Quiz 15: Time Value of Money and Present Value Calculations

If Sloane Joyner invests $10,514.81 now and she will receive $30,000 at the end of 11 years, what annual rate of interest will she be earning on her investment?

Perdue Company has purchased equipment that requires annual payments of $30,000 to be paid at the end of each of the next 6 years.The appropriate discount rate is 12%.What amount will be used to record the equipment?

In present value calculations, the process of determining the present value is called

Hazel Company has just purchased equipment that requires annual payments of $40,000 to be paid at the end of each of the next 4 years.The appropriate discount rate is 15%.What is the present value of the payments?

Present value is based on

The amount you must deposit now in your savings account, paying 6% interest, in order to accumulate $6,000 for a down payment 5 years from now on a new car is

A $10,000, 6%, 5-year note payable that pays interest quarterly would be discounted back to its present value by using tables that would indicate which one of the following period-interest combinations?

The present value of $10,000 to be received in 5 years will be smaller if the discount rate is

If the single amount of $3,000 is to be received in 3 years and discounted at 6%, its present value is

Which of the following discount rates will produce the smallest present value?

If you are able to earn an 8% rate of return, what amount would you need to invest to have $30,000 one year from now?

The amount you must deposit now in your savings account, paying 5% interest, in order to accumulate $10,000 for your first tuition payment when you start college in 3 years is

Peter Johnson invests $35,516.80 now for a series of $5,000 annual returns beginning one year from now.Peter will earn 10% on the initial investment.How many annual payments will Peter receive?

Suzy Douglas has been offered the opportunity of investing $73,540 now.The investment will earn 8% per year and at the end of its life will return $200,000 to Suzy.How many years must Suzy wait to receive the $200,000?

Which of the following accounting problems does not involve a present value calculation?

If you are able to earn a 15% rate of return, what amount would you need to invest to have $15,000 one year from now?

If the single amount of $2,000 is to be received in 2 years and discounted at 11%, its present value is