A $1,000 par value bond with a maturity of five years has a current price of $835 and annual interest payments are $60. what is the yield to maturity?

The cash disbursements for the year were $865,000.To calculate the cash disbursements for the year, we need to use the following formula:

Cash disbursements = Cost of goods sold + Marketing and administrative expenses - Increase in accounts payable + Decrease in merchandise inventory + Increase in accounts receivable

First, we need to calculate the cost of goods sold using the gross profit percentage:

Gross profit = Sales * Gross profit percentage

$1,030,000 * 45% = $463,500

The cost of goods sold can be calcualted as   Sales - Gross profit

$1,030,000 - $463,500 = $566,500

Next, we can calculate the cash disbursements using the formula:

Cash disbursements = $566,500 + $167,000 - (-$49,500) + $28,000 + $54,000

Cash disbursements = $566,500 + $167,000 + $49,500 + $28,000 + $54,000

Cash disbursements = $865,000.Therefore, the cash disbursements  were $865,000.

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The variable overhead rate variance for the month is $78 favorable, which means that the actual variable overhead rate was slightly higher than the standard variable overhead rate, but the company saved money due to the favorable variance.

To calculate the variable overhead rate variance, we need to compare the actual rate per hour with the standard rate per hour and then multiply it by the actual hours worked.

The standard variable overhead rate per hour is $6.10, and the actual variable overhead rate per hour is $6.20.

The variable overhead rate variance is calculated as follows:

Actual Hours Worked x (Actual Variable Overhead Rate - Standard Variable Overhead Rate)

780 x ($6.20 - $6.10) = $78 favorable

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(a) Variables: Independent Variables: Sales, Media Advertising, Price Dependent Variable: Use of Displays

(b) Price Elasticity = -2.841 Price Elasticity = (Change in Quantity Demanded / Change in Price) * (Price / Quantity Demanded)

= (-2.841) * (2.50 / 500) = -0.1136

(c) The price elasticity calculated from the regression analysis should not be entirely trusted for two reasons. First, the sample size of 15 weeks may not be large enough to provide an accurate representation of the overall demand for the shampoo.

Second, the use of displays as the dependent variable may not accurately reflect the demand for the shampoo, as displays may have been placed in stores based on other factors. Thus, the calculated price elasticity may not be an accurate representation of the true demand for the shampoo.

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The University of Michigan studies on leadership identified two distinct styles of leadership, namely, task-oriented and relationship-oriented. A leader who is skilled in the technical aspects of their job will be better equipped to guide and mentor their subordinates.

Task-oriented leaders prioritize the technical aspects of a job, while relationship-oriented leaders prioritize building relationships with their subordinates.

While it may seem counterintuitive for a leader who wants to focus on leadership to prioritize technical aspects, there are situations where a task-oriented approach is appropriate. For example, when dealing with a crisis, a leader needs to focus on the technical aspects of resolving the crisis, such as ensuring that the necessary resources are available and that the problem is solved quickly and efficiently.

Moreover, a leader who is skilled in the technical aspects of their job will be better equipped to guide and mentor their subordinates. They will be able to provide guidance and support that is based on their expertise, and they will be able to better understand the challenges that their subordinates face. This, in turn, will enable them to provide more effective leadership.

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Establishing career paths or planned sequences of advancement for workers through different positions represents internal recruiting

Internal recruiting involves promoting current employees to fill open positions within the organization. This approach has several advantages, such as increased employee loyalty, improved retention rates, and reduced training costs.

Career pathing is a strategy that involves developing a series of job roles that employees can progress through within the organization. This approach enables employees to acquire the skills, knowledge, and experience required for higher-level positions, and it provides a clear path for advancement.

Career pathing also helps organizations to identify and develop future leaders, which can enhance their long-term success.

Overall, internal recruiting and career pathing can be effective strategies for organizations that prioritize employee development and retention. c

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Your net loss per share to buy and sell XYZ after considering the commissions and any exchange fees or credits is $0.0144.

1. Buy XYZ at the best ASK price: $64.98 per share.

Broker's fee: $0.0013 per share.

Exchange fee for removing liquidity: $0.0077 per share.

Total cost to buy one share: $64.98 + $0.0013 + $0.0077 = $64.989 per share.

2. The best BID and ASK prices move lower by one cent each.

New best ASK price: $64.97 per share.

3. Post an order to sell XYZ at the new best ASK price: $64.97 per share.

Exchange credit for adding liquidity: $0.0059 per share.

4. The best BID and ASK prices move higher by one cent each.

Your sell order is executed at the previous ASK price: $64.97 per share.

Broker's fee: $0.0013 per share.

Total amount received for selling one share: $64.97 - $0.0013 + $0.0059 = $64.9746 per share.

5. Calculate the net loss per share.

Net loss = Total cost to buy one share - Total amount received for selling one share

Net loss = $64.989 - $64.9746 = $0.0144 per share.

Your net loss per share to buy and sell XYZ is $0.0144.

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The growth rate projected for Nishi Corporation's common stock is 2.09%.

The dividend growth rate can be calculated using the Gordon Growth Model:

P0 = D1 / (r - g)

where P0 is the current price of the stock, D1 is the dividend per share, r is the required rate of return, and g is the growth rate of dividends.

Rearranging the formula to solve for g, we get:

g = r - (D1 / P0)

Substituting the given values, we get:

g = 10.89% - ($0.79 / $15.62) = 2.09%

Therefore, the growth rate projected for Nishi Corporation's common stock is 2.09%.

Excel screenshot is attached.

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The price of the 18-year STRIPS traded on April 30, 2020, with a yield to maturity of 4.8 percent, can be calculated using the Excel PV function

Calculate the price of the 18-year STRIPS that traded on April 30, 2020, and matures on May 1, 2032, with a yield to maturity of 4.8 percent.

Identify the information provided:- Time to maturity: 18 years, Yield to maturity (YTM): 4.8% ,Calculate the present value (price) of the STRIPS using Excel: Use the formula "=PV(rate, nper, pmt, fv)" in an Excel cell,Enter the YTM (rate) as "0.048" (convert the percentage to a decimal),

Enter the time to maturity (nper) as "18",Leave the "pmt" value blank or enter "0" (as there are no periodic payments for STRIPS), Enter the future value (fv) as "1" (assuming a face value of 1).Interpret the result: The Excel cell will display the present value (price) of the STRIPS.

The price of the 18-year STRIPS traded on April 30, 2020, with a yield to maturity of 4.8 percent, can be calculated using the Excel PV function as described above.

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The correct answer is C. €20 million. This is because the company's comprehensive income for the year is equal to its net income plus the changes in shareholders' equity.

For the given company, net income was €20 million, and the change in shareholders' equity was €27 million (227 million at the end of the year minus 200 million at the beginning of the year).

Thus, the company's comprehensive income for the year was €20 million + €27 million = €47 million. However, since the company paid out €63 million in cash dividends, the company's comprehensive income was reduced to €20 million = €47 million - €63 million. This means that the company's comprehensive income in 2020 was €20 million.

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To provide a more accurate view of future payments, her company incorporates a bad-debts adjustment into the accounts receivable balance.

This adjustment accounts for the possibility of customers defaulting on their payments, allowing the company to estimate the payments they expect to receive. These expected payments are known as the net realizable value of accounts receivable.

This approach is commonly used in businesses that offer financing options, as it helps to minimize the impact of potential bad debt on the company's financial statements.

By accounting for bad debt in this way, the company can present a more realistic view of its financial position and better manage its cash flow.

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As a funds manager, you prefer Trader j's performance due to the higher utility value.

To determine whether trader i and j will buy the same asset, we need to compare the expected utility of each asset for each trader.

For trader i, the expected utility of asset 1 is:

EU(Asset 1) = √103 ≈ 10.15

For asset 2, the expected utility is:

EU(Asset 2) = 0.95√110 + 0.05√0 ≈ 10.29

Therefore, trader i will choose asset 2 because it has a higher expected utility.

For trader j, the expected utility of asset 1 is:

EU(Asset 1) = 1002 ≈ 10,000

For asset 2, the expected utility is:

EU(Asset 2) = 0.95(110)2 + 0.05(0)2 ≈ 10,450

Therefore, trader j will choose asset 2 because it has a higher expected utility.

If you are a funds manager with utility function u(x) = ln √ x, you prefer the trader who has the highest expected utility because that maximizes the overall utility of the investment. In this case, trader j has a higher expected utility for both assets, so you would prefer their performance.

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The combined ratio after dividends for this P&C insurance company is 95%, which is closest to option B, 94%. To determine the combined ratio of a P&C insurance company after dividends, we need to add the loss ratio and the expense ratio and subtract the dividend ratio from the sum.

Loss ratio refers to the amount of claims paid out by an insurance company compared to the premiums it collects. In this case, the loss ratio is 74%, meaning that 74 cents of every dollar collected in premiums is paid out in claims.
Expense ratio refers to the expenses incurred by an insurance company to operate its business, including salaries, rent, and marketing costs. In this case, the expense ratio is 23%, meaning that 23 cents of every dollar collected in premiums is used to cover expenses.
Dividend ratio refers to the portion of profits that the insurance company distributes to its shareholders. In this case, the dividend ratio is 2%, meaning that 2 cents of every dollar collected in premiums is paid out as dividends.
To calculate the combined ratio after dividends, we add the loss ratio and the expense ratio:
74% + 23% = 97%
Then, we subtract the dividend ratio:
97% - 2% = 95%
Therefore, the combined ratio after dividends for this P&C insurance company is 95%, which is closest to option B, 94%. This means that for every dollar collected in premiums, the company pays out 95 cents in claims and expenses, leaving 5 cents as profit before paying out dividends.

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Commodity money is a form of currency that has actual physical value in addition to its monetary value, often taking the form of a commodity such as gold or silver coins.

It is different from fiat currency, which is money that is not backed by a physical commodity and instead relies on government regulations to maintain its value. An example of commodity money is gold coins.

Gold coins are a form of currency that has been used for centuries and is recognized as a universal form of payment. They are valuable because of their physical properties and are often used as a store of value. Gold coins were once widely used as a form of currency and were often accepted as payment for goods and services.

Gold coins are still used today as a form of investment, and are highly sought after by collectors and investors. Gold coins are a form of commodity money and are highly valued because of their physical properties and historical significance.

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Households' labor supply decisions are influenced by all of the following factors except the potential GDP.

Unemployment benefits play a role in labor supply decisions, as they can impact an individual's willingness to search for or accept a job. If the benefits provide enough income to sustain a comfortable living, some people may choose to remain unemployed for longer periods.

Income taxes also affect labor supply decisions, as higher tax rates may discourage individuals from working more hours or seeking additional income sources. People may feel that the additional income is not worth the increased tax burden.

The real wage rate is a crucial factor in labor supply decisions. A higher real wage rate makes work more attractive, leading individuals to supply more labor hours. Conversely, a lower real wage rate might cause people to work fewer hours or seek alternative income sources.

However, the potential GDP, which is an estimate of an economy's maximum output when all resources are fully employed, does not directly influence a household's decision to supply labor. Potential GDP is a macroeconomic concept, primarily used by economists and policymakers to analyze long-term economic trends and potential growth.

In summary, unemployment benefits, income taxes, and the real wage rate are factors that influence households' labor supply decisions, while the potential GDP is not a direct factor in these decisions.

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Complete question:

Households' labor supply decisions are influenced by all of the following except

A. unemployment benefits

B. income taxes

C. the potential GDP

D. the real wage rate

The government mandate of insurance on all people can be seen as both A. Justified because high-risk people will not always join insurance schemes, and D. Justified because without it, insurance schemes may fail.

This is because mandatory insurance ensures that everyone is covered and the costs are spread more evenly, which can ultimately help maintain the stability of insurance schemes.

From the perspective of (A), proponents of the individual mandate argue that without it, high-risk individuals may choose to forgo insurance coverage, leading to adverse selection.

Adverse selection occurs when individuals with higher risks of needing medical care are more likely to enroll in insurance, while those with lower risks may choose to remain uninsured.

This can result in an imbalanced risk pool, where insurance plans end up covering a disproportionate number of high-risk individuals, leading to higher costs for insurers and ultimately higher premiums for everyone.

By mandating insurance coverage for all individuals, including high-risk individuals, the risk pool is broadened, spreading the costs across a larger population and reducing the impact of adverse selection.

Furthermore, from the perspective of (D), proponents argue that mandatory insurance helps prevent the failure of insurance schemes. Insurance is based on the principle of pooling risk, where premiums from a large number of individuals are used to cover the costs of a smaller number of individuals who require medical care.

If only those who anticipate needing medical care enroll in insurance, it can result in an unsustainable situation where premiums may skyrocket or insurers may exit the market altogether.

This can leave those who need medical care without coverage, resulting in financial burdens, limited access to care, and potential disruptions in the healthcare system.

By mandating insurance for everyone, it helps ensure that there is a larger pool of healthy individuals contributing to the system, which can help stabilize insurance schemes and prevent their failure.

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If the U.S. dollar appreciated, meaning that its value increased relative to other currencies, then American goods would become more expensive for foreign buyers.

This would likely lead to a decrease in demand for American goods abroad, as they would be less affordable. Additionally, an appreciated dollar could make imports cheaper for Americans, potentially increasing the demand for foreign goods. Overall, an appreciation of the U.S. dollar could negatively impact American exports and potentially lead to a trade deficit.

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An employer can access stored e-mail communications of employees using the employer's service. This is granted by the Electronic Communications Privacy Act (ECPA). The ECPA allows employers to monitor their employees' electronic communications if they have a legitimate business reason to do so.

This includes monitoring emails sent and received through company email accounts or using company-provided devices. However, employers must still follow certain guidelines, such as notifying employees of monitoring policies and avoiding unreasonable intrusions on privacy.

It is important for both employers and employees to be aware of their rights and responsibilities when it comes to electronic communications in the workplace.

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Tyrone's role as a manager of a bicycle parts factory involves a wide range of responsibilities that fall under the umbrella of operations management.

Based on the responsibilities mentioned, Tyrone can be classified as an operations manager. The primary role of an operations manager is to oversee the production process and ensure that it runs smoothly and efficiently. This includes managing the logistics, quality control, and productivity of the factory.

Tyrone is responsible for transforming raw materials into bicycle parts, which involves managing the entire production process, from planning and designing the factory's operations systems to overseeing the manufacturing process. He must ensure that the production process meets quality standards, is cost-effective, and maximizes efficiency.

Additionally, as a manager, Tyrone must also manage the people involved in the production process, including hiring, training, and supervising employees. He is also responsible for setting goals and targets for the factory, tracking progress towards these goals, and making necessary adjustments to the production process to meet them.

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The correct answer is c. central. While earnings are important in financial statement analysis, an analysis of a company's cash flows is central to credit evaluations and lending decisions.

This is because cash flows reflect the actual cash that a company has on hand to pay its debts, and therefore provide a more accurate picture of its ability to meet financial obligations.  Cash flows provide a more accurate picture of a company's liquidity, solvency, and overall financial health, which are crucial factors for lenders to consider. While banking regulations may require a certain level of cash flow analysis, it is generally considered a fundamental aspect of financial statement analysis.

Thus, if a company's earnings are important in financial statement analysis, with respect to credit evaluations and lending decisions an analysis of its cash flows is c. Central.

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The Black-Scholes-Merton price of the at-the-money DEC call and put are $1.63 and $1.60, respectively.

To calculate the Black-Scholes-Merton price of the at-the-money DEC call and put, we need the following inputs:

Stock price (S) = $25

Strike price (K) = $25

Time to expiration (t) = 50/365

Risk-free rate (r) = (RB + RA) / 2 = (3.19% + 3.16%) / 2 = 3.175%

Annual volatility (σ) = 53%

First, we need to calculate the d1 and d2 terms:

d1 = [ln(S/K) + (r + (σ^2/2)) * t] / (σ * sqrt(t))

d2 = d1 - σ * sqrt(t)

Using the above inputs, we get:

d1 = [ln(25/25) + (0.03175 + (0.53^2/2)) * (50/365)] / (0.53 * sqrt(50/365)) = 0.6813

d2 = 0.6813 - 0.53 * sqrt(50/365) = 0.2609

Next, we need to use the Normal Distribution table to find N(d1) and N(d2). Since the table only provides values for certain probabilities, we need to interpolate between the values. From the table, we find:

N(0.26) = 0.6026

N(0.27) = 0.6064

N(0.68) = 0.7517

N(0.69) = 0.7523

To interpolate N(d1), we have:

N(d1) = N(0.68) + [(N(0.69) - N(0.68)) / (0.69 - 0.68)] * (0.6813 - 0.68) = 0.7517 + [(0.7523 - 0.7517) / (0.69 - 0.68)] * 0.0013 = 0.7519

To interpolate N(d2), we have:

N(d2) = N(0.26) + [(N(0.27) - N(0.26)) / (0.27 - 0.26)] * (0.2609 - 0.26) = 0.6026 + [(0.6064 - 0.6026) / (0.27 - 0.26)] * 0.0009 = 0.6035

Now we can use the Black-Scholes-Merton formula to calculate the call and put prices:

Call price = S * N(d1) - K * e^(-rt) * N(d2)

Put price = K * e^(-rt) * N(-d2) - S * N(-d1)

Substituting the values, we get:

Call price = 25 * 0.7519 - 25 * e^(-0.03175*(50/365)) * 0.6035 = $1.63

Put price = 25 * e^(-0.03175*(50/365)) * N(-0.6035) - 25 * N(-0.7519) = $1.60

Therefore, the Black-Scholes-Merton price of the at-the-money DEC call and put are $1.63 and $1.60, respectively.

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To accumulate $250,000 in 35 years by making equal annual deposits at the end of each year, with a compound interest rate of 10%, the annual deposit needs to be $1,674.14.

To calculate the annual deposit, we can use the formula for the future value of an annuity:

[tex]FV = PMT \times [(1 + r)^n - 1] / r[/tex]

where FV is the future value, PMT is the payment, r is the interest rate, and n is the number of periods.

In this case, we know that FV = $250,000, r = 10%, and n = 35.

Substituting these values into the formula, we can solve for PMT:

$250,000 = PMT x [(1 + 10%)³⁵ - 1] / 10%

$250,000 = PMT x 137.80

PMT = $250,000 / 137.80

PMT = $1,811.60 (annual payment)

However, this solution assumes that the annual payment is made at the beginning of each year.

Since the problem states that the payment is made at the end of each year, we need to adjust the solution by calculating the present value of an annuity due, which is simply the future value of an ordinary annuity multiplied by (1 + r):

[tex]PV = PMT \times [(1 + r)^n - 1] / r \times (1 + r)[/tex]

Substituting the values we have, we get:

PV = $1,674.14 x [(1 + 10%)³⁵ - 1] / 10% x (1 + 10%)

PV = $1,674.14 x 65.44

PV = $109,491.49

Therefore, the amount of the annual deposits needed to accumulate $250,000 in 35 years is $1,674.14.

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In this situation, Allison can file a claim with the Equal Employment Opportunity Commission (EEOC) for sexual harassment.

Allison can file a claim with the Equal Employment Opportunity Commission (EEOC) for sexual harassment because the activity was no longer consensual.

Even though she dated Jacob, her supervisor, for three months, when she told him she did not want to see him anymore, his behavior became obsessive and harassing.

Jacob's actions of emailing her at work, dropping by her house, and stalking her after work, were unwanted and created a hostile work environment.

Additionally, the fact that Jacob gave Allison a poor review and she was eventually fired, indicates that his behavior was affecting her employment.

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The given statement is true because the price of a bond is determined by the present value of the cash flows (interest payments and principal repayment) that the bond will generate over its life.

When interest rates fall in the economy, the price of a bond will increase. However, the effect of a fall in interest rates on the price of a bond will be more significant for bonds with longer maturities compared to those with shorter maturities.

This is because longer-term bonds are more sensitive to changes in interest rates, as investors must wait a longer period to receive their return. Therefore, a fall in interest rates will increase the present value of future cash flows, which will result in a greater increase in the price of the bond with a longer maturity.

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Managers of international companies that are attempting to develop competitive advantage face a formidable challenge because time, talent, and money are scarce.

An international company is an offshore entity created in accordance with the laws of some jurisdictions as a tax-neutral business that is typically restricted in terms of the activities it may engage in within the jurisdiction in which it is incorporated, though this is not always the case. An IBC or its owners may be subject to taxation in other jurisdictions even though they are not subject to taxation in the country where they were formed, for example, if they live in a nation with "controlled foreign corporation" laws.

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The bond's yield to maturity on the day of purchase was 7.51%.

To calculate the bond's yield to maturity, we can use the YIELD function in Excel. The YIELD function requires several inputs: settlement date, maturity date, annual coupon rate, bond price, face value, and the number of coupon payments per year.

Using the given information, we can input the following values into the YIELD function:

Settlement date: April 1, 2022

Maturity date: October 1, 2037

Annual coupon rate: 6.15%

Bond price: $89.11

Face value: $100

Number of coupon payments per year: 2

After inputting these values into the YIELD function, we get a yield to maturity of 7.51%. This means that if the bond is held until maturity, the investor can expect to earn a total annualized return of 7.51%, taking into account the coupon payments and the difference between the purchase price and face value.

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Julia, as a business owner, is right to be concerned about the possibility of her suppliers suing her. She has learned that segregated funds provide creditor protection and has decided to purchase a contract 3 months prior to placing her company into bankruptcy. However, her decision to purchase the contract 3 months before the bankruptcy may not provide her with the protection she was hoping for.

Generally, segregated funds provide creditor protection as they are separate from the individual's estate and cannot be seized by creditors. However, in cases where the segregated funds were purchased with the intent of defeating creditors, the funds may not be protected. This is because such actions are seen as fraudulent and can result in the funds being seized by creditors.

In this case, Julia's purchase of the segregated fund contract 3 months prior to bankruptcy may be seen as an attempt to defeat creditors, and as such, the funds may not be protected. It is important to note that the exact circumstances of each case will be examined before a final decision is made. Overall, while segregated funds may provide creditor protection, it is important to consult with a financial advisor and ensure that any actions taken are legal and ethical.

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Answer:

The annual yield to maturity of the bond is 12%, which means that the bond's cash flows are discounted at a rate of 12% per year. The bond has a 15-year maturity and a $1,000 face value, so it will make 15 annual payments of the same amount. We can use the present value formula to solve for the annual coupon payment:

PV = C / (1 + r)^1 + C / (1 + r)^2 + ... + C / (1 + r)^15 + FV / (1 + r)^15

where PV is the current price of the bond, C is the coupon payment, r is the yield to maturity, and FV is the face value of the bond.

Plugging in the given values:

PV = $659.46

FV = $1,000

r = 12%

n = 15

Solving for C, we get:

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

C = ($659.46 - $1,000 / (1 + 0.12)^15) / [((1 + 0.12)^15 - 1) / 0.12]

C = $79.14

Therefore, the annual coupon payment on this bond is $79.14, which is closest to answer choice d. $79.14.

The adjusting entry required on December 31 is to recognize the accrued salaries expense for the month of December, even though paychecks will not be issued until January 2. This entry will increase the salaries expense and payable accounts on the balance sheet.

The adjusting entry for salaries earned but not yet paid at the end of the period is a common accrual adjusting entry. This entry aims to recognize the expenses incurred in the current period, even though the related cash payments will occur in a future period.

The journal entry to record this adjusting entry on December 31 would be:

Salaries Expense $800,000

Salaries Payable $800,000

This recognizes the expense for December and records the corresponding liability for the unpaid salaries. After this adjusting entry is recorded, the salaries payable balance on the balance sheet will reflect the amount owed to employees for the December salaries, and the salaries expense on the income statement will accurately reflect the total salaries earned by employees during the period.

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The correct question is:

It is December 31, the end of the fiscal year. During December, employees earned $800,000 in salaries, but paychecks do not get issued until January 2.

Which journal entry reflects the adjusting entry needed on December 31?

To calculate the probability that the sample proportion is between 0.10 and 0.12, we need to standardize the sample proportion using the formula:

z = (p - P) / sqrt(P * (1 - P) / n)

p is the sample proportion

P is the population proportion (assumed to be unknown)

n is the sample size

Using this formula, we get:

z1 = (0.10 - 0.5) / sqrt(0.5 * (1 - 0.5) / 20) = -2.83

z2 = (0.12 - 0.5) / sqrt(0.5 * (1 - 0.5) / 20) = -2.12

To find the probability that the sample proportion is between 0.10 and 0.12, we need to find the area under the standard normal distribution curve between z1 and z2. We can use a standard normal distribution table or a calculator to find this probability. For example, using a calculator with a standard normal distribution function, we get:

P(-2.83 < z < -2.12) = 0.0216

Therefore, the probability that the sample proportion is between 0.10 and 0.12 is 0.0216, rounded to 4 decimal places.

Regarding the second part of the question, we cannot answer it because the information provided is incomplete. We need to know the mean and standard deviation of the population, as well as the sample size and level of significance, to determine the probability that the sample mean is less than 12.5.

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To find the probability that the sample mean is less than 12.5, we need to first estimate the population mean and standard deviation. If we do not have this information, we cannot calculate the probability.

To calculate the probability that the sample proportion is between 0.10 and 0.12, we can use the formula for the standard error of the sample proportion:
SEp = sqrt[p(1-p)/n]
where p is the population proportion (unknown) and n is the sample size (given as 20). Since we do not know the population proportion, we can use the sample proportion (p-hat) as an estimate:
p-hat = (number of successes in sample)/n
We can then use the z-score formula to standardize the sample proportion:
z = (p-hat - p)/SEp
Since the sampling distribution of the sample proportion is normally distributed, we can use a standard normal distribution table to find the probability that the sample proportion is between 0.10 and 0.12. We first calculate the z-scores for each end of the interval:
[tex]z1 = (0.10 - p-hat)/SEp\\z2 = (0.12 - p-hat)/SEp[/tex]
Using a standard normal distribution table, we find the area under the curve between these two z-scores, which represents the probability that the sample proportion is between 0.10 and 0.12. The final answer is rounded to 4 decimal places.
Regarding the second part of the question, we can assume that the sampling distribution of the sample mean is normally distributed if either the sample size is large (n > 30) or the population distribution is normal. If we can assume normality, we can use the z-score formula to standardize the sample mean:
[tex]z = (x-bar - mu)/(sigma/sqrt(n))[/tex]
where x-bar is the sample mean, mu is the population mean (unknown), sigma is the population standard deviation (unknown), and n is the sample size (unknown).
To find the probability that the sample mean is less than 12.5, we need to first estimate the population mean and standard deviation. If we do not have this information, we cannot calculate the probability.

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Abby's annual gross income needs to be at least $41,860.44 to qualify for the loan, assuming she has no other debts.

To calculate the annual gross income required for Abby to qualify for this loan, we need to use the Debt-to-Income (DTI) ratio formula:

DTI ratio = (Total monthly debt payments / Monthly gross income) x 100%

We know that Abby's total monthly debt payments are $1,500 ($1,000 for the proposed mortgage, $400 for the car loan, and $150 for the student loan), and her DTI ratio cannot exceed 43%. So we can write:

43% = ($1,500 / Monthly gross income) x 100%

Solving for Monthly gross income:

Monthly gross income = $1,500 / (43% / 100%) = $3,488.37

To calculate the required annual gross income, we simply multiply the monthly gross income by 12:

Annual gross income = $3,488.37 x 12 = $41,860.44

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