Answer:
8%
Explanation:
A firm pays a current dividend of $1
The growth rate is 5%
= 5/100
= 0.05
The current value of the firm's share is $35
Therefore, the required return using the constant growth discount dividend model can be calculated as follows
K = 1×(1+0.05)/35 + 0.05
K= 1×1.05/35 + 0.05
= 1×0.03 + 0.05
= 0.03 + 0.05
= 0.08×100
= 8%
Hence the required return is 8%
An investment adviser representative's friend provides him with a list of 10 prospective clients. The representative agrees to pay his friend a referral fee for each person on the list that opens an account with the adviser. Which statement is TRUE
Answer: C. The arrangement is permitted only if it is in writing between the investment adviser and the friend and the arrangement is disclosed in writing to any customer opening an account
Explanation:
The friend in this case will be ruled to be a Solicitor under SEC Rules as they are referring clients to the Investment Adviser for a fee.
As such this business relationship between the friend and the Investment Adviser representative will fall under SEC Rule 206(4)-3 Cash payments for client solicitations. This rule makes it clear amongst other things that the investment adviser will have to prepare a written disclosure document which will inform any customer opening an account of the agreement between the adviser and his friend.
An appraiser estimated the replacement cost new of a building at $560,000. The building has an estimated economic life of 40 years and an estimated remaining life of 30 years. What is the current value of the building
Answer:
The answer is $420,000
Explanation:
To find the amount of depreciation being charged years, we use the following formula:
Cost of the asset ÷ number of useful life
Cost of the asset - $560,000
Number of useful life - 40 years
$560,000 ÷ 40 years
$14,000.
The asset has 30 years remaining, that means it has used 10 years. So the accumulated depreciation is $140,000
And the current value of the building now is $420,000($560,000 - $140,000)
The current value of the building is $420000
The estimated economic life is 40 years, hence after 40 years the value of the house would be 0.
Since the estimated remaining life is 30 years. Hence:
Percentage value of house = 30 remaining years / 40 economic year
Percentage value of house = 0.75 * 100 = 75%
The current value of the building = 75% * $560000 = $420000
The current value of the building is $420000
Find out more on current value at: https://brainly.com/question/24304697
Roybus, Inc., a manufacturer of flash memory, just reported that its main production facility in Taiwan was destroyed in a fire. Although the plant was fully insured, the loss of production will decrease Roybus's free cash flow by $175 million at the end of this year and by $61 million at the end of next year. a. If Roybus has 37 million shares outstanding and a weighted average cost of capital of 12.6%, what change in Roybus's stock price would you expect upon this announcement? (Assume that the value of Roybus's debt is not affected by the event.) b. Would you expect to be able to sell Roybus stock on hearing this announcement and make a profit? Explain.
Answer:
a) the fire and all the events that are related to it should decrease Roybus's stock by $5.50
b) The market is pretty quick to adjust to bad news, specially when they are single isolated events. There is a minimum chance that you might be able to make some money by selling your stocks to someone that hasn't heard about the fire and its negative consequences (not a regular trader or outside the market), but it would be extremely rare for it to happen. When such extraordinary events happen, it is common for stocks to be traded after market hours, so when the market opens the next day, the price will already be adjusted.
Explanation:
the total decrease in Roybus's market value = ($175,000,000 / 1.126) + ($61,000,000 / 1.126²) = $155,417,407 + $48,111,960 = $203,529,367
the decrease will negatively affect stock price by -$203,529,367 / 37,000,000 stocks = -$5.50 per stock
True or False:
Transactions that result in significant investing and financing activities bu that do not involve cash are reported either directly after the statement of cash flows or in a note to the financial statements
Answer: True
Explanation:
Transactions that do not increase or decrease cash, but that result in significant investing and financing activities, are reported as noncash activities either directly after the cash flow statement or in a note to the financial statements.
It is true that In cash-flow statement, any transaction that do not involve cash are reported directly after the statement or in a note to the financial statements
Non-cash activities includes depreciation amortization, unrealized gain, unrealized loss etc
In accounting, non-cash investing or financing activities are required to be disclosed in the footnotes to the financial statements or within the cash flow statement.
Therefore, It is true that In cash-flow statement, any transaction that do not involve cash are reported directly after the statement or in a note to the financial statements.
Read more about Non-cash activities here
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Jason has a loan that requires a single payment of $6,000 at the end of 3 years. The loan's interest rate is 10%, compounded semiannually. How much did Jason borrow? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
Answer:
Jason borrowed $4,4,77.29
Explanation:
In order to calculate this, let we will use the formula for the future value on an invested amount, semiannually, yielding interest at a certain interest rate. This is done as follows:
[tex]FV\ =\ PV(1+\frac{r}{n} )^{(n\times t)}[/tex]
where:
FV = future value = $6,000 (loan repayment)
PV = present value = amount borrowed = ??
r = interest rate = 10% = 10/100 = 0.1
n = number of compounding periods per year = 2
t = time = 3 years
[tex]6,000\ =\ PV(1+\frac{0.1}{2} )^{(2\times 3)}\\6,000\ =\ PV(1+ 0.05)^{6}\\6,000\ =\ PV(1.05)^{6}\\6,000\ =\ PV (1.340096)\\diving\ both\ sides\ by\ 1.340096\\PV = \frac{6,000}{1.340096} \\PV = \$4,477.29[/tex]
Therefore, Jason borrowed $4,4,77.29
Martin works as a pizza delivery person.He parks his bike outside Regalia Inc.to deliver an order.Meanwhile,a damaged book rack in Regalia,which is situated on the first floor of the building,falls down through an open window and crashes on his bike.However,no one admits to having seen the rack fall.Can Martin recover against Regalia for negligence?
A) Martin can recover only if he finds a witness who saw the book rack crashing on the bike.
B) Martin can recover if he can prove that book racks do not fall out of windows in the absence of negligence and that Regalia Inc. had exclusive control of the rack prior to the fall.
C) Martin will be unable to recover because parking under an open floor window amounts to contributory negligence and he is therefore liable for the accident too.
D) Martin will be unable to recover because parking under an open window amounts to assumption of risk.
Answer:
B) Martin can recover if he can prove that book racks do not fall out of windows in the absence of negligence and that Regalia Inc. had exclusive control of the rack prior to the fall.
Explanation:
Negligence is defined as a situation where a person does not take due care and conduct oneself like a reasonable person in a given circumstance.
When a defendant is negligent he will be held responsible for damage that results from his negligence.
In this scenario Martin's parked his bike and makes a delivery, meanwhile a book rack falls on his bike.
Martin's can only recover against Regalia if he proves that he was not negligent in any way, and that Regalia had control of the rack before the fall.
For example if Martins did not park his bike in a designated parking spot, he can be seen to be negligent. In that case he will not be able to recover against Regalia.
What are examples of career fields Skills USA prepares students for? Check all that apply.
health science
O education
agriculture
construction
manufacturing
transportation
information technology
public safety
Answer:
everything except education and agriculture
Explanation:
hope this helps •_•
Answer:
Everything except education and ariculture
Explanation:
edu 2021
The treasurer of Riley Coal Co. is asked to compute the cost of fixed income securities for her corporation. Even before making the calculations, she assumes the aftertax cost of debt is at least 3 percent less than that for preferred stock.
Debt can be issued at a yield of 11.0 percent, and the corporate tax rate is 20 percent. Preferred stock will be priced at $60 and pay a dividend of $6.40. The flotation cost on the preferred stock is $6.
a. Compute the aftertax cost of debt. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
b. Compute the aftertax cost of preferred stock. (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
c. Based on the facts given above, is the treasurer correct?
Answer:
a. Compute the after tax cost of debt.
after tax cost of debt = 11% x (1 - tax rate) = 11% x 0.8 = 8.8%
b. Compute the after tax cost of preferred stock.
after tax cost of preferred stock = cost of preferred stock (no taxes are deducted for paying preferred dividends since they are paid in capital)
cost of preferred stocks = $6.40 / ($60 - $6) = $6.40 / $54 = 11.85%
c. Based on the facts given above, is the treasurer correct?
the difference = 11.85% - 8.8% = 3.05%, so the treasurer was right
Based on your case knowledge, to what extent do you agree or disagree with the following statement - "Kay Whitmore - Kodak CEO, had an understanding of Kodak's potential in the PC market. This was illustrated by her strong engagement with Bill Gates and Microsoft."
1. Strongly Agree
2. Mildly Agree
3. Neither Agree nor Disagree
4. MIldly Disagree
5. Strongly Disagree
6. Not Applicable
Answer:
3. Neither Agree nor Disagree
Explanation:
The reason was that the Kay Whitmore's engagement with Bill Gates and Microsoft has not much impacts on the potential of Kodak's products to exploit additional opportunities in Microsoft hence statement in consideration is not a one side argument as it is doubtful position.
So I am neither agreeing nor disagreeing with the statement hence the option 3 is correct here.
Costco and other big box price clubs charge a membership fee on top of the price of goods sold to members. This is an example of
Answer: Service Charge
Explanation: a service charge goes toward the day to day running costs of a company, used to cover things like building costs, insurance, employee compensation. It is how companies like Costco are able to pass along reduced price products to members.
Margin on price as a percentage is the expression of how much you mark your product up by to arrive at your retail price. True False
Answer:
False
Explanation:
The margin on price refers to a percentage by taking a difference between the gross profit and the selling price
Here gross profit comes by
= Selling price - cost price
Now in the cost price we added some markup percentage i.e most probably equivalent to the retail price
Hence, the given statement is false
Quality is primarily related to satisfaction viewpoint of:___________.
a. Customer Manufacturer
b. Service provider
c. General public
d. all of above
Answer: Consumer
Explanation:
Quality has to do with the standard by which a product is being compared with other similar products.
Quality is primarily related to satisfaction viewpoint of consumers. If consumers are not satisfied with a particular product, it will have a negative impact on the sale of the product hence the product quality must be taken into consideration in order to enable consumers to buy such product.
Suppose that Dunkin Donuts reduces the price of its regular coffee from $2 to $1 per cup, and as a result, the quantity sold per day increased from 10 to 40. Over this price range, the price elasticity of demand for Dunkin Donuts’ regular coffee is:
Answer:price elasticity of demand for Dunkin Donuts’ regular coffee is 1.8
Explanation: Using the midpoint formnulae
Price elasticity of Demand =percentage change in quantity demanded/ Percentage change in price.
Percentage change in quantity = new quantity - old quantity / (new quantity + old quantity)/2 x 100
= 40-10/(40+10)/ 2 = 30 /25 = 1.2 x 100 =120%
Percentage change in price = new price - old price / new price + old price)/2 x 100
= 1- 2 / (1+2)/2= -1/1.5x 100 = -66.67 %
Price elasticity of Demand =percentage change in quantity demanded/ Percentage change in price.
= 120%/-66.67%= -1.79 = -1.8
For Price elasticity of demand, the sign is not included and the basis for elasticity is on the value itself . here we can conclude that the Price elasticity of demand for Dunkin donut is 1.8 and elastic because a fall in price led to an increase in amount being sold.
Vijay Inc. purchased a 3-acre tract of land for a building site for $420,000. On the land was a building with an appraised value of $120,000. The company demolished the old building at a cost of $12,000, but was able to sell scrap from the building for $1,500. The cost of title insurance was $900 and attorney fees for reviewing the contract was $500. Property taxes paid were $3,000, of which $500 covered the period subsequent to the purchase date. The capitalized cost of the land is:
Answer:
$433,900
Explanation:
The computation of the capitalized cost of the land is shown below:-
Capitalized cost of the land = Purchase price + Demolition of building + Title insurance + Attorney fee + Property taxes covered during the period - Scrap value from the building
= $420,000 + $12,000 + $900 + ($3,000 - $500) - $1,500
= $420,000 + $12,000 + $900 + $2,500 - $1,500
= $435,400 - $1,500
= $433,900
On January 2 2018, Maxwell Furniture purchased display shelving for $8,100 cash, expecting the shelving to remain in service for five years. Maxwell depreciated the shelving on a double-declining-balance basis, with $1,800 estimated residual value. On October 31, 2019, the company sold the shelving for $2,700 cash.
Requirement:
Record both the depreciation expense on the shelving for and its sale in . Also show how to compute the gain or loss on the disposal of the shelving.
Answer: Please find answers in explanation column
Explanation:
Double declining depreciation rate = 1/n x 2
= 1/5 x 2= 2/5 = 0.4 x 100 = 40 %
Carrying value = if depreciation rate = 40 % , then begining value = 100-40=60%
Depreciation expense for 2019 = Carrying value x depreciation nrate x period(jan- oct) = $8,100 x 60% x 40% x 10/12 = $1,620
Journal entry to record Depreciation expense
Accounts Debit Credit
Depreciation expense $1,620
Accumulated depreciation--Display shelving $1,620
Carrying value / Ending balance of shelving at October, 2019= cost - depreciation
8,100 - 8,100 x 40% + 1620 = 8,100 - 4,860= $3240
Gain/ Loss = Sale - the ending balance of the carrying value of the asset
$2700 - $3240= -540= $540 loss
Journal to record shelving for and its sale in .
Accounts Debit Credit
Cash $2700
Accumulated depreciation--
Display shelving (3240 +1620) $4860
loss on sale of asset $540
Shelving $8,100
IOP Company purchased a machine on 1/1/22 costing $500. Estimated life was 5 years; estimated salvage value was $100. In 2025, IOP discovered that the bookkeeper correctly used straight-line depreciation, but erroneously used an estimated life of 8 years in computing depreciation for the first 3 years of life. The Prior Period Adjustment to be recorded in 2025 will be:
Answer:
The Prior Period Adjustment to be recorded in 2025 will include a $90 debit as adjustment to Retained Earnings
Explanation:
Correct depreciation would have been = ($500-$100)/5 = $80
Depreciation charged wrongly as ($500-$400)/8 = $50
Therefore depreciation has been charged short by $30 for three years, thereby reflecting income greater by $30 each year for 3 years.
Since due to wrong depreciation retained earnings is higher by $90, therefore we have to debit retained earnings by $90
Dragon Sports Inc. manufactures and sells two products, baseball bats and baseball gloves. The fixed costs are $620,000, and the sales mix is 40% bats and 60% gloves. The unit selling price and the unit variable cost for each product are as follows: Products Unit Selling Price Unit Variable Cost Bats $90 $50 Gloves 105 65 a. Compute the break-even sales (units) for the overall enterprise product, E.
Answer:
$15,500 units
Explanation:
For the computation of break-even sales (units) for the overall enterprise product, E first we need to follow some steps which is shown below:-
Contribution margin = (Selling price - Variable costs)
For Bats $90 - $50
= $40
For Gloves = $105 - $65
= $40
Overall contribution margin = (40 × 40%) + (40 × 60%)
= $40
a.Break-even point = Fixed costs ÷ Contribution margin
= $620,000 ÷ 40
= $15,500 units
The following information describes the production activities of Mercer Manufacturing for the year.
Actual direct materials used 28,000 lbs. at $4.90 per lb.
Actual direct labor used 8,650 hours for a total of $174,730
Actual units produced 51,600
The budgeted standards for each unit produced are 0.50 pounds of direct material at $6.85 per pound and 10 minutes of direct labor at $21.20 per hour.
1. Compute the direct materials price and quantity variances. Do not round intermediate calculations.
2. Compute the direct labor rate and efficiency variances. Indicate whether each variance is favorable or unfavorable. Do not round intermediate calculations.
Answer:
Actual Quantity = 28,000
Actual Price = 4.90
Standard Quantity = 25,800
Standard Price = 4.85
1)a. Direct Material Price variance = (Standard price – Actual Price)*Actual Quantity
= (4.85 - 4.90) * 28,000
= $1,400 U
b. Direct Material Quantity variance = (Standard Quantity – Actual Quantity)*Standard price
= (51,600*0.5 - 28,000)*4.85
= $10,670 U
2) a. Direct Labor Rate Variance = (Standard Rate – Actual Rate)*Actual Hours
= (21.20 - 20.2) * 8,650
= $8,650 F
b. Direct Labor Efficiency variance = (Standard Hours – Actual Hours)*Standard rate
= (51,600*1/6 - 8,650) * 21.20
= $1,060 U
The cash register tape for Bluestem Industries reported sales of $28,372.00.
Record the journal entry that would be necessary for each of the following situations. (a) Cash to be accounted for exceeds cash on hand by $52.00. (b) Cash on hand exceeds cash to be accounted for by $26.50. (Credit account titles are automatically indented when amount is entered. Do not indent manually. Round answers to 2 decimal places, e.g. 52.75.)
Answer:
Bluestem Industries
Journal Entries
a) Cash to be accounted for exceeds cash on hand by $52.00
Debit Cash Shortage $52.00
Credit Cash Account $52.00
To record the cash shortage.
b) Cash on hand exceeds cash to be accounted for by $26.50
Debit Cash Account $26.50
Credit Cash Overage $26.50
To record the cash overage.
Explanation:
Handling cash in Bluestem Industries will occasionally give rise to cash shortages and cash overages. The best practise is to enact a company policy to guide actions and decisions with respect to cash shortages and overages. And then the accounting for these will be in accordance with the policy. However, the problem of shortages and overages may be pointing at other underlying problems involved in cash handling. Where only the shortages are reported frequently, then the company may need to find ways to minimize cash handling, e.g. using credit cards to receive payments and refunding employees for expenses through bank accounts.
Specialty Auto Parts Company uses the indirect method to prepare its statement of cash flows. Refer to the following information for 2018: Net cash provided by operating activities: $108,000 Net cash used for investing activities: ($118,500) Net cash provided by financing activities: $16,000 If the cash balance at the beginning of the year was $13,200, what is the ending cash balance? A. $18,700 B. $13,200 C. $10,500 D. $5,500
Answer: $18,700
Explanation
Net cash provided by the operating activities = $108,000
Add: Net cash provided by the financing activities = $16,000
Less : The net cash used for the investing activities = $118,500
The net increase in Cash will now.be:
= ($108,00 + $16,000) - $118,500
= $5,500
Add: Cash at the beginning of the year. This will be:
= $5500 + $13,200
= $18,700
Ending cash balance will be $18700
You have a $46,000 portfolio consisting of Intel, GE, and Con Edison. You put $20,800 in Intel, $10,400 in GE, and the rest in Con Edison. Intel, GE, and Con Edison have betas of 1.3, 1, and .8, respectively. What is your portfolio beta? Multiple Choice 1.071 0.976 0.824 1.393
Answer: 1.071
Explanation:
The portfolio beta is the weighted average of the constituent stock betas.
Intel Weight
= 20,800/46,000
= 0.45217
GE Weight
= 10,400/46,000
= 0.22609
Con Edison
= (46,000 - 20,800 - 10,400) / 46,000
= 0.32174
Portfolio Beta;
= (0.45217 * 1.3) + (0.22609 * 1) + (0.32174 * 0.8)
= 0.587821 + 0.22609 + 0.257392
= 1.071303
= 1.071
Builtrite has calculated the average cash flow to be $16,000 with a standard deviation of $4000. What is the probability of a cash flow being less than $9000? (Assume a normal distribution.)
Answer:
4%
Explanation:
For Builtrite, we can find the probability of cash flows by using the following formula:
Z = (X - C) / S
Average Cash Flow is $16000 which denoted by "C"
Standard Deviation is $4000 and is denoted by "S"
And
For cash flows that are less than $9000 which is denoted by X in the equation, "Z" can be calculated as under:
Z = (X - C) / S = ($9,000 - $16,000) / $4,000 = -1.75
As Z is less than -1.75, now we can see that the probability from the Z-table is 4% for -1.75.
Hence the probability of cash flow below $9,000 is 4%.
An investment adviser places large block trades for securities positions that are being purchased for its customers' accounts in order to lower its commission costs. The trades are often executed piecemeal, at different prices. The adviser, after being confirmed that the entire block has been filled, allocates the shares to its accounts. As a favor to its most valuable employees, the adviser allocates the shares purchased at the lowest prices to its employees' accounts; and then allocates the remaining shares to its customer accounts pro-rata. The adviser has disclosed its allocation method only to its employees. Which statement is TRUE
Answer: The investment adviser has breached its fiduciary duty because it has not disclosed its method of allocating shares to its customers
Explanation:
The options to the question are:
a. The investment adviser has breached its fiduciary duty to its customers because the block order must be executed at one price, not in pieces at differing prices
b. The investment adviser has breached its fiduciary duty because it has not disclosed its method of allocating shares to its customers
c. The investment adviser has not breached its fiduciary duty because it has disclosed its method of allocating shares to its employees
d. The investment adviser has not breached its fiduciary duty to customers because it has obtained trade executions for customers at lower commission costs.
Based on the scenario in the question, it should be noted that the investment adviser has breached its fiduciary duty because it has not disclosed its method of allocating shares to its customers.
Fiduciary duty is a legal obligation whereby a party has to work in the best interest of the other party and should also be trustworthy but in this situation, this isn't thw case.
The present value of $10,000 to be received in 10 years, discounted at an annual rate of 6.78%, is closest to:
Answer:
PV= $5,189.21
Explanation:
Giving the following information:
The present value of $10,000 to be received in 10 years, discounted at an annual rate of 6.78%.
To calculate the present value, we need to use the following formula:
PV= FV/(1+i)^n
PV= 10,000/(1.0678^10)
PV= $5,189.21
The following data were reported by a corporation: Authorized shares 38,000 Issued shares 33,000 Treasury shares 12,500 The number of outstanding shares is:
Answer:
20,500 shares
Explanation:
Authorized shares= 38,000
Issued shares= 33,000
Treasury shares= 12,500
Therefore, the number of outstanding shares can be calculated as follows
Outstanding shares= Issued shares-Treasury shares
= 33,000-12,500
=20,500
Hence the number of outstanding shares is 20,500
A stock is bought for $24.00 and sold for $26.00 one year later, immediately after it has paid a dividend of $1.50. What is the capital gain rate for this transaction?
Answer:
8.33%
Explanation:
A stock is bought for $23.00
The stock is sold for $26 after one year
The dividend paid is $1.50
Therefore, the capital gain rate can be calculated as follows
Capital gain= P1-Po/Po
= 26-24/24
= 2/24
= 0.0833 ×100
= 8.33%
Hence the capital gain rate for this transaction is 8.33%
A customer redeems 1,000 shares of ABC Fund on Wednesday, June 14th. Under the provisions of the Investment Company Act of 1940, the customer must be paid the money no later than:
Answer:
Wednesday, June 21st
Explanation:
In this scenario, since the customer redeemed the shares on Wednesday, June 14th then he must be paid before Wednesday, June 21st. This is 7 days after the redemption. According to section 22 article (e) of the Investment Company Act of 1940, all companies are prevented from postponing the date of payment for more than seven days as stated below.
(e) No registered investment company shall suspend the right
of redemption, or postpone the date of payment or satisfaction upon
redemption of any redeemable security in accordance with its terms
for more than seven days after the tender of such security to the
company or its agent designated for that purpose for redemption
You can use the discounted cash flow method to estimate the cost of a company’s internal equity when the company ______________. g
Answer:
Pays any amounts of dividends
Explanation:
Moorcroft sales are 40% cash and 60% credit. Credit sales are collected 20% in the month of sale, 50% in the month following sale, and 26% in the second month following sale; 4% are uncollectible. Moorcroft purchases are 50% cash and 50% on account. Purchases on account are paid 40% in the month following the purchase and 60% in the second month following the purchase.Prepare a schedule of expected collections from customers for June.
Answer:
The budgeted sales are missing, so I looked for them. I found the following question, hopefully it will be similar:
Month Sales
April $300,000
May $320,000
June $370,000
Schedule of expected collections
For the month of June, 202x
Cash sales during June = $370,000 x 40% = $148,000
Collection from June's credit sales = $222,000 x 20% = $44,400
Collection from May's credit sales = $192,000 x 50% = $96,000
Collection from April's credit sales = $180,000 x 26% = $46,800
Total cash collections during June = $335,200
Assume that your parents wanted to have a 170,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 6.5% per year on their investmenets.Required:a. How much would they have to save each year to reach their goal?b. If they think you will take five years instead of four to graduate to graduate and decide to have $140,000 saved just in case, how much more would they have to save each year to reach their new goal?
Answer:
a. They will have to save $5,245.28 each year to reach their goal of $170,000.
b. They will have to save $925.63 less to reach their new goal of $140,000.
Note: The answer to part b is based on the information in the question. Therefore, the correct answer is "they will have to save $925.63 less" not "save more" as suggested in the question. Kindly confirm this from your teacher.
Explanation:
a. How much would they have to save each year to reach their goal?
Since the saving started on your first birthday to have $170,000 saved, it implies the saving will be on your every birthday for 18 years. Therefore, the relevant formula to use to determine this is the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * {[(1 + r)^n - 1] / r} ................................. (1)
Where,
FV = Future value of the amount after your 18th birthday = $170,000
M = Yearly saving to have $170,000 = ?
r = interest rate = 6.5%, 0.065
n = number of years this savings will be made = 18
Substituting the values into equation (1) and solve for M, we have:
$170,000 = M * {[(1 + 0.065)^18 - 1] / 0.065}
$170,000 = M * 32.4100673759666
M = $170,000 / 32.4100673759666
M = $5,245.28
Therefore, they will have to save $5,245.28 each year to reach their goal of $170,000.
b. If they think you will take five years instead of four to graduate to graduate and decide to have $140,000 saved just in case, how much more would they have to save each year to reach their new goal?
First, we have to calculate how much they will save each year, by also using the Future Value (FV) for calculating an Ordinary Annuity as follows:
FVn = Mn * {[(1 + r)^n - 1] / r} ................................. (1)
Where,
FV1 = New future value of the amount after your 18th birthday = $140,000
M1 = New yearly saving to have $140,000 = ?
r = interest rate = 6.5%, 0.065
n = number of years this savings will be made = 18
Substituting the values into equation (1) and solve for M1, we have:
$140,000 = M1 * {[(1 + 0.065)^18 - 1] / 0.065}
$140,000 = M1 * 32.4100673759666
M1 = $140,000 / 32.4100673759666
M1 = $4,319.65
Therefore, they will have to save $4,319.65 each year to reach their goal of $140,000.
To obtain difference in yearly savings, we have:
Difference in yealy saving = M - M1 = $5,245.28 - $4,319.65 = $925.63
Since $5,245.28 each year to reach their goal of $170,000 is greater than $4,319.65 each year to reach their goal of $140,000, it therefore implies that they will have to save $925.63 less to reach their new goal of $140,000.
