Answer:
Results are below.
Explanation:
Giving the following information:
Present value(PV)= $7,000
Number of periods (n)= 4 years
Interest rate (i)= 8% annually
To calculate the future value of the investment, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 7,000*(1.08^4)
FV= $9,523.42
Now, the interest earned:
Interest earned= FV - PV
Interest earned= 9,523.42 - 7,000
Interest earned= $2,523.42
How do you make decision for the yourself?what are the things that you consider before making a decision
Answer: I consider what's best for me first and what would he beneficiary to others
Explanation:
Making decisions for oneself should be directed most times to growth. Questions like; "how would this affect me or how will this benefit those around me".
When we consider what benefits us and others around us we tend to make the best decision which helps out growth and bring out the best in others.
The optimal portfolio for an individual investor is represented by the point that lies on the Question 7 options: lowest possible utility curve and connects to the efficient frontier. utility curve which is just tangent to the right side of the feasible set of risk-return options. utility curve which is just tangent to the efficient frontier. utility curve which represents the highest possible rate of return within the feasible set of risk-return options.
Answer:
Utility curve which is just tangent to the efficient frontier.
Explanation:
The optimal portfolio of the investor is the maximum gain for the maximum risk. If risk factor is increased beyond optimal level it does not necessarily means that returns will also increase. Efficient frontier is curved because there is diminishing marginal utility to risk. For every additional unit of risk added into the portfolio gains a smaller amount of return.
Macmillan Toys Inc. is looking to expand internationally and wishes to develop a new product line that is highly localized while keeping their cost structure below that of their rivals. Macmillan Toys Inc. has been successful with implementing a blue ocean strategy in their main strategic business units and as such wishes to pursue a ________ strategy for their international operations.
Answer:
Multi domestic strategy
Explanation:
From the question we were informed that Macmillan Toys Inc. which is looking to expand internationally and wishes to develop a new product line that is highly localized while keeping their cost structure below that of their rivals. Macmillan Toys Inc. has been successful with implementing a blue ocean strategy in their main strategic business units and as such wishes to pursue a Multi domestic strategy
strategy for their international operations. Multi-domestic strategy can be regarded as strategy utilized by companies whereby a firm ensure that there is maximum local responsiveness through the customization of their product offering as well as marketing strategy so that it can along with the match different national conditions.
72. Sociology is a. the systematic study of group and team processes. b. the systematic study of the production, distribution and consumption of goods and services. c. the systematic study of the processes by which groups of people make decisions. d. the systematic study of the processes in the organization and workplace that improve the performance and well being of people.
Answer:
a. the systematic study of group and team processes.
Explanation:
Sociology is "the systematic study of group and team processes."
This is based on the idea that sociology is a systematic discipline or study of society and how it relates within itself.
Society is a combination of groups of people within a given geographical, or professional area, all of which functioning at various levels to make better living conditions or outcomes.
Hence, it is the study that involves a group and how they co-exist.
A county that did not previously have a property tax levies a property tax for $900,000 on January 1, 2020 for the budget year January 1 to December 31, 2020. The county collected $875,000 during 2020, $20,000 during January 1 through February 28, 2021, and the remaining $5,000 in June 2021. What adjustment is needed to the data reported in the governmental fund financial statements to prepare the government-wide statements
Answer: See explanation
Explanation:
The adjustment is needed to the data reported in the governmental fund financial statements to prepare the government-wide statements will be:
Deferred revenues—property taxes
5,000
Revenues—property taxes
5,000
Deferred revenue, in this case refers to the advance payments that a company receives for the goods that are to be delivered in the future.
ASAP PLEASEEE!!! If the price level were to rise from 160 to 200, in what direction and by how much would the value of a dollar change?
Answer:
- Downward direction
- The change in dollar value is 0.00125
Explanation:
Given
[tex]P_1 = 160[/tex]
[tex]P_2 = 200[/tex]
Required
Direction and value of dollar change
Value is calculated using
[tex]V = \frac{1}{P}[/tex]
When [tex]P_1 = 160[/tex], the value is:
[tex]V_1 = \frac{1}{160}[/tex]
[tex]V_1 = 0.00625[/tex]
When [tex]P_2 = 200[/tex], the value is:
[tex]V_2 = \frac{1}{200}[/tex]
[tex]V_2 = 0.005[/tex]
So, we have:
[tex]V_1 = 0.00625[/tex]
[tex]V_2 = 0.005[/tex]
Notice that [tex]V_1 > V_2[/tex]
i.e. the initial value is greater than the new value
Hence, the value of dollar moves down
The change in value is:
[tex]\triangle V = |V_2 - V_1|[/tex]
[tex]\triangle V = |0.005 - 0.00625|[/tex]
[tex]\triangle V = |- 0.00125|[/tex]
Remove absolute sign
[tex]\triangle V = 0.00125[/tex]
The change in dollar value is 0.00125
Johnson- Schmitt gave several dogs to Dispenza to find good homes for them. Dispenza did not find good homes for them, but rather kept them on his property in such deplorable conditions that they were eventually seized by the sheriff, turned over to the local SPCA, and adopted out to other families. Johnson- Schmitt later sued the county claiming unlawful conversion of her property( the dogs). Did Johnson- Schmitt have any property right in the dogs at the time they were seized?
Answer:
John-Schmitt had property right in the dogs at the time they were seized.
She had the right to dispose of her private property (dogs) and also to delegate Dispenza to dispose of her property (dogs). She was still in this right of disposition to her property before they were seized. Therefore, she could sue the country (right to property right enforcement) for unlawful conversion of her dogs.
Explanation:
The right of disposition or transferability is one of the property rights, including the right of possession, the right of control, the right of exclusion, the right of enforcement, and the right to derive income from the property. The right of transferability means that property rights should be transferable from one owner to another in a voluntary exchange. She can enforce her property rights.
An employee sued her employer in federal court for sexual harassment. The jury returned a verdict in favor of the employer. Three months after the verdict, the employee's attorney received an anonymous letter stating that a key document presented at trial by the employer had been altered. The employee moved for relief from judgment, alleging that a document presented by her employer at trial had been altered. Assuming that the employee can show that the alteration was intentional, how should the court rule
Answer:
Grant the employee's motion, because fraud and misconduct of an adverse party are proper grounds for relief, and she filed within the appropriate time frame.
Explanation:
An employee sued her employer in federal court for sexual harassment. The jury returned a verdict in favor of the employer. Three months after the verdict, the employee's attorney received an anonymous letter stating that a key document presented at trial by the employer had been altered. The employee moved for relief from judgment, alleging that a document presented by her employer at trial had been altered. Grant the employee's motion, because fraud and misconduct of an adverse party are proper grounds for relief, and she filed within the appropriate time frame.
Lucia wants to use a safe deposit box. What will this process MOST likely include? A. visiting a bank and paying a fee B. uploading documents to a computer C. getting someone to cosign for his box D. applying for a loan
Answer: Answer is A,,,,,,,,,,
Lucia wants to use a safe deposit box. The process MOST likely include is visiting a bank and paying a fee. Thus the correct option is A.
What is a Bank?A bank is referred to as a financial institution that allows an individual to deposit and withdraw cash and allow them to borrow funds with a fixed interest rate for investment.
The bank provides you with a key when you rent a deposit box from them, and you must apply it in combination with a second "guard key" kept by a bank employee to open the box.
In the given case, it is explained that Lucia wants to use a safe deposit box. Banks are referred to as financial institutions that are connected or authorized by Government due to which they are considered as safe.
Therefore, option A is appropriate.
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What is TRUE about debt-for-nature swaps?Question 50 options: The wealthy nation's debt is forgiven when it donates money to conservation efforts. In exchange for land rights in protected areas, wealthy nations forgive part of a developing nation's debt. Wealthy nations forgive a part of a developing nation's debt if that nation promises to pay a percentage of any ecotourism profit to the wealthy nations. Part of a developing nation's debt is forgiven by wealthy nations if they promise to protect natural areas in their country. Part of a developing nation's debt is forgiven by wealthy nations if they promise to give the wealthy nations exclusive rights to vacation in protected areas.
Answer:
Part of a developing nation's debt is forgiven by wealthy nations if they promise to protect natural areas in their country.
Explanation:
Biodiversity
This is simply defined as arrays or wide ranges of plant and animal life in a particular habitat/world. It is also known as the types of organisms in a given area, the genetic differences within a population, the types of species in a community, or the different types of communities in an ecosystem.
Endangered Species
This is simply known as species whose are limited in numbers. That is the species is at risk of extinction.
Debt for nature swap
This was a form of deal made by agencies such as the World Bank with third world countries. The deals focus was that they will cancel their debt if the country will set aside a certain amount of their natural resources.
It is also known as the forgiveness or clearing of international debt in exchange for nature protection in developing countries.
Advantage and disadvantage of debt-for-nature swaps
Advantage
(1) There is an expansion of purchasing power cash donations by converting.
(2) It create an avenue for channeling spending toward goals of local environmentalist group.
3. Reduce outstanding debt etc.
Disadvantage
(1) It legitimizes debt, admitting must be repaid or repurchased.
(2) The Willingness of the debtor government to undergo the swap is small to its interest in spending local currency generated on specific environmental projects, less accuracy that funding will forthcoming than debt-for-equity swaps.
A bond par value is $1,000 and the coupon rate is 6.3 percent. The bond price was $946.86 at the beginning of the year and $984.56 at the end of the year. The inflation rate for the year was 2.1 percent. What was the bond's real return for the year
Answer:
8.36%
Explanation:
The computation of the real rate of return is given below:
Coupon amount = $1,000 × 6.3% = $63
Return on price is
= $984.56 - 946.86
= $37.7
Now
Nominal rate of return =( (63 + 37.7) ÷ 946.86 ) × 100
= 10.64%
And, finally
Real rate of return = (1+ nominal return) ÷ (1+inflation) - 1
= (1.1064 ÷ 1.021) - 1
= 8.36%
Keepsake Collectibles focuses its marketing efforts on high-income buyers of unique collectible items. The firm realizes that the number of buyers in this segment of the collectible market is small. However, they are confident that this approach will be profitable since these buyers will pay premium prices for their unique products and superior customer service. Keepsake's approach is an example of:
Answer:
niche marketing.
Explanation:
From the question we are informed about Keepsake Collectibles which focuses its marketing efforts on high-income buyers of unique collectible items. The firm realizes that the number of buyers in this segment of the collectible market is small. However, they are confident that this approach will be profitable since these buyers will pay premium prices for their unique products and superior customer service. Keepsake's approach is an example of niche marketing.
The niche market can be regarded as subset of market whereby specific product is the target or been focused.
The market niche gives the description about product features and focus on satisfying particular market needs, it also focus on satisfying price range as well as production quality and also the demographics required for target. It can be regarded as small market segment
The testator, a widower, had his attorney prepare a will according to the testator's instructions. The attorney mailed the will to the testator. The testator signed the will in the presence of his father, and asked his father to sign the will as a witness, which his father did. The testator then showed the will to his adult son, told him that the signature on the will was his, and asked his son to sign the will as a witness as well. The testator's will devised $100,000 to his adult son, with the remainder of the testator's estate passing to his other two sons in equal shares. When the testator died, the will was offered for probate. The testator was survived by the father, the adult son, and the other two sons. As witnesses, the father and the son are asked to testify to the facts concerning the execution of the will. Should the testator's will be admitted to probate?
Answers:
A. Yes, because the father and the adult son both testified to the facts concerning the execution of the will.
B. No, because the father and the adult son did not sign the will in each other's presence.
C. Yes, because the will had the necessary two witnesses.
D. No, because the father and the adult son are also beneficiaries.
Answer: No, because the father and the adult son did not sign the will in each other's presence
Explanation:
The testator's will should not be admitted to probate because the father and the adult son did not sign the will in each other's presence.
A will requires a writing such that the testator will sign in the joint presence of two attesting witnesses. It should also be noted that both witnesses understand the importance of that act of the testator and then sign in each other's presence.
four factors that affect the productivity of an office worker
Answer:
not enough sleep
no breakfast
noise
distractions
On January 1, year 1, Eber Co. leased equipment under a four-year capital lease. The present value of minimum lease payments is $348,680. The equipment had a five-year economic life and a $20,000 guaranteed residual value. The equipment reverted to the lessor at the end of the lease. What amount should Eber report as depreciation expense at December 31, year 1?
Answer:
$87,170
Explanation:
Calculation to determine What amount should Eber report as depreciation expense at December 31, year 1
Using this formula
Depreciation expense at December 31, year 1=Present value of minimum lease payments /Capital lease years
Let plug in the morning
Depreciation expense at December 31, year 1= $348,680 / 4 years
Depreciation expense at December 31, year 1= $87,170
Therefore Depreciation expense at December 31, year 1 is $87,170
Which of these correctly describes the statute of limitations as it applies to real estate? Unset starred question A wronged party can initiate a court action at any time after closing but before reselling the property. The buyer has the time between the inspection and closing to initiate a court action against the seller. There’s a time limit for a wronged party (buyer or seller) to initiate a court action. The seller has a limited time after closing to disclose any known defects with the property.
Answer:
There’s a time limit for a wronged party (buyer or seller) to initiate a court action.
Explanation:
The best statement that correctly describes the statute of limitations as it applies to real estate is the "There’s a time limit for a wronged party (buyer or seller) to initiate a court action."
This is evident in the fact that depending on the bone of contention or the main issues, there are certain but limited times required for the wronged party to go through litigation to resolve the issue.
For example in California, United States, there are Six Primary Statutes of Limitation apply in Real Estate Sales Transactions and Litigation and each has limited time with 4years of Limitations for Breach of Contract, and 2 years for Limitations for Actions Against a Real Estate Broker Agent, etc.
A government will likely ____________________________ to encourage investment in technology R&D by private firms? reduce R&D grants to nonprofit organizations reduce R&D grants to universities spend more on R&D in government laboratories implement fiscal policy establishing tax incentives NEXT
Answer:
implement fiscal policy establishing tax incentives
Explanation:
Discretionary fiscal policies are deliberate steps taken by the government to stimulate the economy in order to cause the economy to move to full employment and price stability more quickly than it might otherwise.
Discretionary fiscal policies can either be expansionary or contractionary
Tax incentives are taxes designed to encourage certain economic activities
Tax incentives include :
1. tax holidays - the company is exempted from paying tax for a specified period
2. tax reduction - the amount of tax that would be paid is reduced for a specified period.
Tax incentives would reduce the cost of undertaking a particular activity and this can encourage private firms to become involved in that activity
A housecleaning agency was given a key to a customer's house so that the agency could have its employees clean while the homeowner was away. After a maid sent by the agency had finished and left the homeowner's house, she went back because she had forgotten her cigarettes. She neglected to lock the door when she left the second time because she was already late for the next job. When the homeowner returned after a few days away, she discovered that her house had been ransacked and several items of jewelry stolen. The front door was open, and there were no signs of forced entry. If the homeowner brings an action against the agency that employed the maid, what is the likely result
Answer:
C. She will prevail, because the maid's failure to lock the door created the risk that someone might enter and take the homeowner's valuables.
Explanation:
Based on the argument presented above, the homeowner will likely prevail against the agency because, the maid whibis an employee of the cleaning agency got the home exposed by failing to get the doors locked which might have allowed unwarranted entry into the building. The fact that there was no forced entry through any of the entry channels and the disappearance of valuables gives the homeowner a stronger case to make in this scenario in her case against the agency.
Find out stock value of the company with following dividend plans: $ 3, $ 4, $ 5, $6 , $7 for the first five years, then a final liquidating dividend of $60 at year 6. Assume discount rate for this stock is 15%. Find out the current stock value .
The current stock price will be $41.77
The current stock value will be the present value of all the dividends over the five years in question and then the present value of the liquidating dividend in the 6th year.
Present value = Dividend / ( 1 + rate) ^ year it was paid
Present value of all the dividends = ( 3 / (1 + 15%)) + (4 / (1 + 15%)²) + (5 / (1 + 15%)³) + (6 / ( 1 + 15%)⁴) + (7 / ( 1 + 15%)⁵) + ( 60 / ( 1 + 15%)⁶)
= $41.77
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For the year ended December 31, 2021, Norstar Industries reported net income of $965,000. At January 1, 2021, the company had 1,070,000 common shares outstanding. The following changes in the number of shares occurred during 2021: Apr. 30 Sold 85,000 shares in a public offering.May 24 Declared and distributed a 5% stock dividend.June 1 Issued 96,000 shares as part of the consideration for the purchase of assets from a subsidiary.Required:Compute Norstar's earnings per share for the year ended December 31, 2021. (Enter your answers in thousands. Round "EPS" answer to 2 decimal places. Do not round intermediate calculations.) Numerator = ? Denominator = ?Earnings per share = ?
Answer:
0.78
Explanation:
The computation of the earning per share is given below;
= $965,000 ÷ 1,239,000
= 0.78
The 1,239,000 comes from
= 1,070,000 × 12 ÷ 12 + 85000 × 8 ÷ 12 + 96,000 × 7 ÷ 12 + (1,070,000 + 56,667) × 5%
= 1,070,000 + 56,667 + 56,000 + 56,333
= 1,239,000
Karen has been asked to head a team at work that is charged with finding new ways to develop products for their marketing group. She has asked her team members to begin exploring approaches that have worked in the past and to identify approaches that have not worked before. Karen wants her team members to start the process of Group of answer choices
Answer:
C. adopting a questioning attitude.
Explanation:
Since in the question it is mentioned that they have to develop the products for the marketing group so for this they started to exploring the approaches that worked on the past and identified those approaches that does not worked before so here she wants that the process should be begins by adopting the questioning attitude that means they are capable to identify the errors facing in a activities they perfomed
Therefore the option c is correct
op down and bottom up estimating both use parametric (ratio) estimating, the difference is that... Multiple choice question. Top down looks at the project as a total unit, whereas bottom up looks at individual tasks. There is no difference, the method is the same for both techniques.
Answer:
Top down looks at the project as a total unit, whereas bottom up looks at individual tasks.
Explanation:
in the case when the top down and the bottom up predicted the usage of the parametric ratio that could be expected that the difference should be that the top down recognize the project and treated as the total unit while on the other hand the bottom up recognized the project on the person to person task or indiviudal task
Therefore the above statement should be considered
If a business is using factors of production 100% efficiently, the plot will be on the curve. However, most business efficiency falls inside the
curve. Why is this?
A. They are not making efficient use of their factors
of production.
B. They are making over 100% efficient use of their
factors of production.
C. They are making inequitable use of their factors
of production.
Answer: A. They are not making efficient use of their factors of production.
Explanation:
Production Possibilities Curve helps in capturing opportunity cost and scarcity when an economy produces two goods or services.
It should be noted that the points on the interior of the PPC simply means that the economy is inefficient. The points on the PPC implies that the economy is efficient, while the points beyond the PPC simoky means that they are unattainable.
Based on the question, the production points inside the curve simply implies that the economy isn't producing at its comparative advantage, and therefore, they are not making efficient use of their factors of production.
What people used before paper money was created
Answer:
Before money was invented, goods and services were exchanged through bartering or using commodities like salt, cattle, or grains.
Explanation:
People used metal objects as money to exchange goods and services as early as 5000 B.C. Paper money in the United States dates back to 1690 and represented bills of credit or IOUs.
When environmentalists recognized that politicians were not going to pass stricter legislation and regulations, they changed their tactics to force change. According to the Layzer article in the chapter, these new tactics included: I. Eco-terrorism - bombing pipelines and factories. II. Collaboration with businesses - create partnerships to improve environmental impacts. III. Public relations campaigns - go public with their accusations and encourage consumers to demand change. IV. Work internally through shareholders to try to change corporate disclosures
Answer:
II. Collaboration with businesses - create partnerships to improve environmental impacts.
III. Public relations campaigns - go public with their accusations and encourage consumers to demand change.
IV. Work internally through shareholders to try to change corporate disclosures
Explanation:
Since the environmentalists recognized that politicians were not going to pass stricter legislation and regulations, the tactics employed in order to force change include:
Ii. Collaboration with businesses - create partnerships to improve environmental impacts.
III. Public relations campaigns - go public with their accusations and encourage consumers to demand change.
IV. Work internally through shareholders to try to change corporate disclosures.
Therefore, the correct options are II, III and IV.
The Fair Credit Reporting Act, or Title VI of the Consumer Credit Protection Act of 1968, requires that lenders do all of the following EXCEPT which? Keep all credit information confidential. Obtain authorization from a consumer in order to seek the customer’s credit information. Reveal the sources of the credit information to the consumer. Give consumers copies of their credit reports.
Answer:
Give consumers copies of their credit reports.
Explanation:
In Business, credit can be defined as money or a loan facility agreed upon by a lender and a borrower, who is obligated to repay the lender at a specified date mostly with interest depending on the terms and conditions.
The Fair Credit Reporting Act, or Title VI of the Consumer Credit Protection Act of 1968 is a federal law of the United States of America that was enacted by the 91st US Congress and signed into law by President Richard Nixon on the 26th of October, 1970.
The main purpose of this federal law is to protect consumer reports and information by promoting accuracy, fairness, and privacy collected by consumer reporting agencies.
However, the Fair Credit Reporting Act, or Title VI of the Consumer Credit Protection Act of 1968, do not require that lenders give consumers copies of their credit reports.
Which of the following steps in the management decision-making process does not generally involve the managerial accountant? Determine possible courses of action. Make the appropriate decision based on relevant data. Prepare internal reports that review the impact of decisions. None of these answers are correct.
Answer:
Make the appropriate decision based on relevant data.
Explanation:
Management involves the control, planning and organization of the affairs of a business firm.
Basically, the management of an organization is saddled with the responsibility of planning, organizing, controlling and staffing within the organization.
The four (4) main management activities are;
I. Organizing
II. Controlling
III. Motivating.
IV. Planning.
Managerial accounting also known as cost accounting is an accounting technique focused on identification, measurement, analyzing, interpretation, and communication of financial information to managers for better decisions making and pursuit of the organization's goals. Thus, it's an accounting system that is used by an organization to report both monetary and nonmonetary information.
In the management decision-making process, making the appropriate decision based on relevant data does not generally involve the managerial accountant.
A managerial accountant is an individual who is saddled with the responsibility of gathering and communication of financial information to managers for better decisions making.
Karin does not want her supervisor to know that the employees she is in charge of are not fulfilling their obligations, fearing the information will make her look like a bad manager to her boss. She decides not to tell her supervisor and deal with it on her own. This type of message distortion is
Answer:
general distortion.
Explanation:
According to the above scenario, it is correct to state that the type of message distortion is a general distortion, which occurs when a message is transmitted differently to a given receiver, in order to minimize negative situations, such as in a relationship of hierarchical work.
In the question we see that Karin distorted the facts so as not to displease her supervisor, so the general distortion is very recurrent in these situations. In order to reduce distortion, it is ideal that in power relations there is an opening for assertive and non-punitive communication, where trust and professional ethics prevail.
Johnson is an executive vice president at Conecom Hardware. He researches a proposal by a larger company, Openlane Hardware, to combine the two companies. By analyzing past performance, conducting focus groups, and interviewing Openlane employees, Johnson concludes that Openlane has poor profit margins, sells shoddy merchandise, and treats customers poorly. What actions should Johnson and Conecom Hardware take
Answer: Turn down the acquisition offer and prepare to resist a hostile takeover.
Explanation:
Since Johnson analysed the past performance of Openlane hardware and found out that past performance, conducting focus groups, and interviewing Openlane employees, Johnson concludes that the company has poor profit margins, sells shoddy merchandise, and treats customers poorly, then Johnson and Conecom Hardware should turn down the acquisition offer and prepare to resist a hostile takeover.
In this case, the merge between the companies will have a negative impact on Johnson and Conecom hardware due to the fact that the company has a bad reputation already and this can have an effect on Conecom. Therefore, the acquisition offer should be turned down.
(a) Find the present and future value of an income stream of per year for a period of years if the interest rate, compounded continuously, is . Round your answers to two decimal places. Present value Enter your answer; Present value = $ 70825 Future value Enter your answer; Future value = $ 70825 (b) How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places. The amount from the income stream is Enter your answer; The amount from the income stream is $ 90000 . The amount from the interest is Enter your answer; The amount from the interest is $ 116769.6 .
The question is incomplete. The complete question is :
(a) Find the present and future value of an income stream of $8000 per year for a period of 10 years if the interest rate, compounded continuously, is . Round your answers to two decimal places.
Present value ___
Future value ___
b). How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places.
The amount from the income stream is __
The amount from the interest is ___
Solution :
Since the interest is compounded continuously, the formula used is :
[tex]$P=\int_0^{m} s(t)\ e^{-rt}\ dt$[/tex]
P = present value, B = future value
[tex]$B=Pe^{rt}$[/tex]
Given :
S = $ 8000, r = 4% = 0.04, m = 10
[tex]$P=\int_0^m \ 8000. e^{-0.04t} \ dt$[/tex]
[tex]$P=\int_0^{10} \ 8000. e^{-0.04t} \ dt$[/tex]
According to the fundamental theorem of calculus,
[tex]$\int_a^b f(x) = F(b) -F(a)$[/tex]
[tex]$\int e^{ax}\ dx = \frac{e^{ax}}{a}$[/tex]
[tex]$P=\int_0^{10} \ 8000. e^{-0.04t} \ dt$[/tex]
[tex]$P=8000 \times \left[ \frac{e^{-0.04t}}{-0.04}\right]^{10}_0$[/tex]
Uploading the limits,
[tex]$P=\frac{8000}{-0.04} \times \left[ e^{-0.04 \times 10} - e^{-0.04 \times 0} \right]$[/tex]
P = -200000 [-0.32967]
P = 65935.99
Therefore, Present value, P = $65936
[tex]$B=Pe^{rt}$[/tex]
[tex]$B=65936 \times e^{10 \times 0.04}$[/tex]
[tex]B= 98364.9[/tex]
So, future value , B = $ 98365
Amount of the future value from the income stream,
[tex]$=\int_0^m s(t) \ dt$[/tex]
[tex]$=\int_0^{10} 8000 \ dt$[/tex]
[tex]$=8000 \times [t]_0^{10}$[/tex]
= 8000 x 10
= $ 80000
Simply, S(t) x t = 8000 x 10 = $ 80,000
The difference between the future value and the value of future value from the income stream provides the future value from the interest.
B - 80,000 = 98,365 - 80,000
So, the future value from the interest = $ 18,365
