Answer:
PV= $774.54
Explanation:
Giving the following information:
Future value= $1,000
Number of periods= 5*365= 1,825 days
Interest rate= 0.05/365= 0.00014
To calculate the initial investment, we need to use the following formula:
PV= FV / (1+i)^n
PV= 1,000 / (1.00014^1,825)
PV= $774.54
Yoshi Co.'s 12/31/2020 inventory on a FIFO basis was $980,000. The following information is available: Estimated selling price is $1,020,000; Estimated cost of disposal is $40,000; Normal profit margin is $120,000; and Current replacement cost is $900,000. At 12/31/2020, assuming Yoshi uses the loss method, what amount of loss should Yoshi record from applying LCM
Answer:
Yoshi Co.
The amount of loss that Yoshi Co. should record from applying LCM (the lower of Cost or Market price) is:
$40,000
Explanation:
a) Data and Calculations:
FIFO inventory on 12/31/2020 = $980,000
Current replacement cost = $900,000
Net realizable value = $980,000 ($1,020,000 - $40,000)
Normal profit margin = $120,000
Loss to be recognized based on current replacement cost = FIFO purchase cost minus Current replacement cost
= $80,000 ($980,000 - $900,000)
b) Under the US GAAP (generally accepted accounting principles) of prudence and conservatism, the loss of $80,000 must be recognized in the current period, since the inventory will be booked at $900,000, its current replacement cost, which is lower than the FIFO purchase cost of $980,000.
The expected return on the market portfolio is 12%, and the relevant risk-free rate is 4.2%. What is the equity premium?
Answer:
7.8%
Explanation:
The expected return on the market portfolio is 12 percent
The risk free rate is 4.2 percent
Therefore the equity premium can be calculated as follow
= expected return - risk free rate
= 12% - 4.2%
= 7.8%
Hence the equity premium is 7.8%
Delphi Company uses job-order costing. It applies overhead to jobs using a predetermined overhead rate based on machine-hours. At the beginning of the year, Delphi estimated that it would work 37,000 machine-hours and incur $222,000 in manufacturing overhead cost. The following transactions were recorded for the year: a. Raw materials were issued for use in production, $367,000 ($345,000 direct and $22,000 indirect). b. Employee costs were incurred: direct labor, $309,000; indirect labor, $44,000; and administrative salaries, $155,000. c. Factory depreciation, $175,000. d. Selling costs, $140,000. e. Manufacture overhead was applied to jobs. The actual machine hours for the year were 35,000 hours. a. Compute the total manufacturing overhead cost applied to jobs during the year.
Answer:
Allocated MOH= $210,000
Explanation:
First, we need to calculate the predetermined overhead rate:
Predetermined manufacturing overhead rate= total estimated overhead costs for the period/ total amount of allocation base
Predetermined manufacturing overhead rate= 222,000/37,000
Predetermined manufacturing overhead rate= $6 per machine hour
Now, we cal allocate overhead:
Allocated MOH= Estimated manufacturing overhead rate* Actual amount of allocation base
Allocated MOH= 6*35,000
Allocated MOH= $210,000
On October 1, 2020, Jackson Chemical was identified as a potentially responsible party by the Environmental Protection Agency. Jackson's management along with its counsel have concluded that it is probable that Jackson will be responsible for damages, and a reasonable estimate of these damages is $5,000,000. Jackson's insurance policy of $9,000,000 has a deductible clause of $500,000. How should Jackson Chemical report this information in its financial statements at December 31, 2020
Answer:
Jackson Chemical should report the $5,000,000 loss because we don't know if the insurance will actually pay out the policy.
Explanation:
Jackson chemical has to report $500,000 loss associated with the deductible would be accrued as liability in the company's financial statements at Dec 31, 2020 since it is probably that Jackson will be responsible for the damages.
$500,000 is the amount of the insurance policy's deductible Jackson will have to pay to receive the policy's benefits, which will cover the reasonably estimated damages.
The following information pertains to Lightning Inc., at the end of December: Credit Sales $ 20,000 Accounts Payable 10,000 Accounts Receivable 12,900 Allowance for Uncollectible Accounts 400 credit Cash Sales 20,000 Lightning uses the aging method and estimates it will not collect 7% of accounts receivable not yet due, 15% of receivables up to 30 days past due, and 48% of receivables greater than 30 days past due. The accounts receivable balance of $12,900 consists of $10,000 not yet due, $1,600 up to 30 days past due, and $1,300 greater than 30 days past due. What is the appropriate amount of Bad Debt Expense
Answer:
$1,164
Explanation:
Calculation for the appropriate amount of Bad Debt Expense
Bad Debt Expense= (10,000 * 0.07) + (1,600 * 0.15) + (1,300 * 0.48) =
Bad Debt Expense=700+240+624
Bad Debt Expense=1,564 -400
Bad Debt Expense=$1,164
Therefore the appropriate amount of Bad Debt Expense will be $1,164
If there was a 24% chance of having a contract signed to purchase a home in any one month and there were 55 homes on the market, what would be the probability that exactly 15 of them would have a contract signed during this month?
a. 10.3%
b. 24.0%
c. 66.7%
d. 23.0%
Answer:
a. 10.3%
Explanation:
P∝F of Binomial distribution is given as Pr.(x=x) = nCxP^x(1-p)^(n-x)
P = 0.24, n= 55, x =15 Note: C = Combination
Pr.(x = 15) = 55"C"15(0.24)^15(0.76)(55-15)
Pr.(x = 15) = 55"C"15(0.24)^15(0.76)^40
Pr.(x = 15) = 0.1026
Pr.(x = 15) = 10.26%
Pr.(x = 15) = 10.3%
[Same investments as the prior question] Suppose two local start-ups are raising funding by issuing shares of equity at $10,000 per share. One start-up is a whiskey distillery; the other is a beer brewery. You estimate the expected returns on your investment to be 50% over five years in both cases. You also believe that the likelihood of being paid out $20,000 per share is greater with the distillery than with the brewery. Suppose now that you hold a portfolio of many other risky assets, and that this would be your N 1 investment. Which investment do you prefer to make, the distillery or the brewery
Answer:
you should purchase the brewery's stock
Explanation:
First of all, as investors we should always try to maximize our returns while avoiding risks. It is really hard to balance both, but we must compare stocks to see which may represent a higher gain while posing the lesser or same risk.
Initial investment in each = $10,000 (equal for both)expected returns over 5 years = $5,000 (equal for both)but there is a higher possibility of the distillery's stock being more valuable, and that makes a difference.Both stocks seem equally risky, but they are not. When you calculate expected returns, you multiply the possible returns by their probability. I'm not sure how they calculated the expected returns of the above stocks, but the following can help you understand my point:
stock B return probability expected return
great 100% 25% 25%
normal 50% 50% 25%
bad 0% 25% 0%
total 100% 50%
stock D return probability expected return
great 100% 30% 30%
normal 50% 40% 20%
bad 0% 30% 0%
total 100% 50%
Both stocks have the same expected return, but stock B is less risky because the chance of being a bad investment is lower.
Mr. C made the following gifts: $12,000 to a university to pay tuition costs for his niece. An undeveloped tract of land to his sister that had an adjusted basis to Mr. C of $4,000 and a fair market value of $25,000. Various shares of stock to his wife that had an adjusted basis to Mr. C of $15,000 and a fair market value of $40,000. Mr. C did not consent to gift-splitting. What is the total amount of taxable gifts
Answer:
$10,000
Explanation:
Gifts are only taxed when their fair market value is higher than $15,000. Any gifts made to your spouse are not taxable. Gift taxes are calculated on a per person base, as long as they do not exceed the lifetime exemption (which is $11.58 million).
The tuition costs of her niece are not taxable since they are less than $12,000. The stocks given to his wife are not taxable either. The only taxable gift is the land given to his sister which had a FMV of $25,000. The taxable amount = $25,000 - $15,000 = $10,000
Alfarsi Industries uses the net present value method to make investment decisions and requires a 15% annual return on all investments. The company is considering two different investments. Each require an initial investment of $15,600 and will produce cash flows as follows: End of Year Investment A B 1 $ 8,600 $ 0 2 8,600 0 3 8,600 25,800 The present value factors of $1 each year at 15% are: 1 0.8696 2 0.7561 3 0.6575 The present value of an annuity of $1 for 3 years at 15% is 2.2832 The net present value of Investment B is:
Answer:
Net present value $1,363.50
Explanation:
The computation of the net present value of B is shown below:
Year Cash flows PVIFA factor at 15% Present value
0 -$15,600 1 -$15,600
1 0 0.8696 0
2 0 0.7561 0
3 25,800 0.6575 $16,963.50
Net present value $1,363.50
On January 1, 2020, Echo Company issued $550,000, 16 year, 9%, annual, callable bonds for $475,000. On December 31, 2025, Echo Company redeemed (called) the bonds at 102. REQUIRED: 1. Prepare the Journal Entry to record the Issuance of the Bond 2. Determine the amount of the Discount/Premium that is still not amortized (using the Straight-Line Method) 3. Prepare the Journal Entry to record the Retirement (Redemption) of the Bond.
Answer:
1. Prepare the Journal Entry to record the Issuance of the Bond
January 1, 2020, bonds issued at a discount
Dr Cash 475,000
Dr Discount on bonds payable 75,000
Cr Bonds payable 550,000
2. Determine the amount of the Discount/Premium that is still not amortized (using the Straight-Line Method)
total bond life = 16 years, 5 years have passed
amortization of bond discount per coupon payment = $75,000 / 16 = $4,687.50
so $51,562.50 have not been amortized yet
3. Prepare the Journal Entry to record the Retirement (Redemption) of the Bond.
Before being able to redeem the bonds, the remaining discount must be amortized:
December 31, 2025, amortization of bond discount
Dr Interest expense 51,562.50
Cr Discount on bonds payable 51,562.50
the journal entry to record the redemption of the bonds
December 31, 2025, bonds redeemed at a loss
Dr Bonds payable 550,000
Dr Loss on retirement of debt 11,000
Cr Cash 561,000
The primary focus for financial accounting information is to provide information useful for: Investing decisions Credit decisions a. Yes Yes b. Yes No c. No Yes d. No
Answer:
a. Yes yes
Explanation:
The primary focus for financial accounting information is to provide useful information to investors for decision making. This is to enable both present and potential investors have prior knowledge and state of affairs of the company or business they want to spend their money on.
However, in the long run, the focus for financial accounting would also include providing useful information for credit decisions. The aforementioned would only occur if a company is able to generate profit hence providing rate of returns to their investors.
Answer:
MAYBE
Explanation:
yes + no = maybe
Forrester Company is considering buying new equipment that would increase monthly fixed costs from $425,000 to $445,500 and would decrease the current variable costs of $60 by $15 per unit. The selling price of $100 is not expected to change. Forrester's current break-even sales are $1,140,000 and current break-even units are 11,400. If Forrester purchases this new equipment, the revised break-even point in dollars would be:
Answer:
Break-even point (dollars)= $810,000
Explanation:
Giving the following information:
Fixed costs= $445,500
Unitary variable cost= $45
Selling price= $100
To calculate the break-even point in dollars, we need to use the following formula:
Break-even point (dollars)= fixed costs/ contribution margin ratio
Break-even point (dollars)= 445,500 / [(100 - 45) / 100]
Break-even point (dollars)= $810,000
You will invest $25,000 in an ice cream shop your sister is starting. You expect to triple your investment in six years. What is the rate of return that you have in mind? (Rounded to the nearest percent.)
Answer:
r = 20.09%
Explanation:
we can use the future value formula to calculate the expected rate of return:
future value = present value x (1 + r)ⁿ
future value = $25,000 x 3 = $75,000present value = $25,000n = 6$75,000 = $25,000 x (1 + r)⁶
(1 + r)⁶ = $75,000 / $25,000 = 3
⁶√(1 + r)⁶ = ⁶√3
1 + r = 1.2009
r = 0.2009 = 20.09%
Bob has been investing $4,000 in stock at the end of every year for the past 8 years. If the account is currently worth $45,000, what was his annual return on this investment?a. 10.61%b. 10.91%c. 8.81%d. 9.55%e. 9.07%
Answer:
d. 9.55%
Explanation:
we can use the future value of an annuity formula to calculate Bob's annual return:
future value = annual contribution x FV annuity factor
future value = $45,000
annual contribution = $4,000
FV annuity factor = ?
FV annuity factor = future value / annual contribution = $45,000 / $4,000 = 11.25
FV annuity factor = [(1 + i)ⁿ - 1] / i
11.25 = [(1 + i)⁸ - 1] / i
11.25i = (1 + i)⁸ - 1
solving this problem is really complicated, but there is a much simple way to do it:
e) 11.25 x 0.0907 = (1 + 0.0907)⁸ - 1
1.020375 ≠ 1.0028
d) 11.25 x 0.0955 = (1 + 0.0955)⁸ - 1
1.0744 = 1.0744 ⇒ this option is correct
ear Net Income Profitable Capital Expenditure 1 $ 14 million $ 8 million 2 18 million 11 million 3 9 million 6 million 4 20 million 8 million 5 23 million 9 million The Hastings Corporation has 2 million shares outstanding. (The following questions are separate from each other). a. If the marginal principle of retained earnings is applied, how much in total cash dividends will be paid over the five years? (Enter your answer in millions.)
Answer:
$42 Million
Explanation:
The computation of the total cash dividend is shown below:-
Year Net Income Profitable capital Expenditure Dividends
1 $14 Million $8 Million $6 Million
2 $18 Million $11 Million $7 Million
3 $9 Million $6 Million $3 Million
4 $20 Million $8 Million $12 Million
5 $23 Million $9 Million $14 Million
Total cash dividends $42 Million
Cutting flights and declaring bankruptcy are long-run decisions. What impact would you predict these actions would have on the airlines remaining in business?
Answer:
Follows are the solution to this question:
Explanation:
The declaration of bankruptcy as well as flight cutting reduces the amount for flights and also the flight sin operation leading to both a supply reduction. While the business continued, its other airlines will have an increased engagement and thus higher prices and will be seeing recovery for both the airline industry over an amount of time.
Exercise 17-5 Assigning costs using ABC LO P3 Xie Company identified the following activities, costs, and activity drivers for this year. The company manufactures two types of go-karts: Deluxe and Basic. Activity Expected Costs Expected Activity Handling materials $ 625,000 100,000 parts Inspecting product 900,000 1,500 batches Processing purchase orders 105,000 700 orders Paying suppliers 175,000 500 invoices Insuring the factory 300,000 40,000 square feet Designing packaging 75,000 2 models Assume that the following information is available for the company’s two products for the first quarter of this year. Deluxe Model Basic Model Production volume 10,000 units 30,000 units Parts required 20,000 parts 30,000 parts Batches made 250 batches 100 batches Purchase orders 50 orders 20 orders Invoices 50 invoices 10 invoices Space occupied 10,000 sq. ft. 7,000 sq. ft Models 1 model 1 model Required: Compute activity rates for each activity and assign overhead costs to each product model using activity-based costing (ABC). What is the overhead cost per unit of each model? (Round activity rate and average OH cost per unit answers to 2 decimal places.)
Answer:
Instructions are below.
Explanation:
First, we need to calculate the activity rate for each activity:
Predetermined manufacturing overhead rate= total estimated overhead costs for the period/ total amount of allocation base
Handling materials= 625,000/100,000= $6.25 per part
Inspecting product= 900,000/1,500= $600 per batch
Processing= 105,000/700= $150 per order
Paying suppliers= 175,000/500=$350 per invoice
Insuring the factory= 300,000/40,000= $7.5 per square feet
Designing packaging= 75,000/2= $37,500 per model
Now, we can allocate overhead to each model:
Allocated MOH= Estimated manufacturing overhead rate* Actual amount of allocation base
Deluxe:
Handling materials= 6.25*20,000= 125,000
Inspecting product= 600*250= 150,000
Processing= 150*50= 7,500
Paying suppliers= 350*50= 17,500
Insuring the factory= 7.5*10,000= 75,000
Designing packaging= 37,500*1= 37,500
Total allocated overhead= $412,500
Basic:
Handling materials= 6.25*30,000= 187,500
Inspecting product= 600*100= 160,000
Processing= 150*20= 3,000
Paying suppliers= 350*10= 3,500
Insuring the factory= 7.5*7,000= 52,500
Designing packaging= 37,500*1= 37,500
Total allocated overhead= $444,000
Finally, the unitary overhead:
Deluxe= 412,500/10,000= $41.25
Basic= 444,000/30,000= $14.8
Under the allowance method for uncollectible accounts, the journal entry to record the estimate of uncollectible accounts would include a credit to
Answer and Explanation:
The journal entry to record the estimation of the uncollectible accounts is shown below:
Bad debt expense XXXX
To Allowance of doubtful debts XXXX
(Being the estimation of the uncollectible account is recorded)
Here the bad debt expense is debited as it increases the expenses account and credited the allowance as it decreased the assets
Hence, the same is to be considered
On April 1, 2020, the City of Southern Ponds issued $5,000,000 in 4% general obligation, tax supported bonds at 101 for the purpose of constructing a new police station. The premium was transferred to a debt service fund. A total of $4,990,000 was used to construct the police station, which was completed before December 31, 2020, the end of the fiscal year. The remaining funds were transferred to the debt service fund. The bonds were dated April 1, 2020, and paid interest on October 1 and April 1. The first of 20 equal annual principal payments of $250,000 is due April 1, 2021. In addition to reporting Bonds Payable and (unamortized) Bond Premium in the government-wide Statement of Net Position, how would the bond sale be reported
Answer:
$100,000
$350,000
Explanation:
The bond sale be reported as debt service expenditures for 2020 and 2021 can be calculated as follows
The Amount would be reported as debt service expenditures for 2020
= $5,000,000 x 4% x 1/2 year
= $100,000
The amount would be reported as debt service expenditures for 2021
= $5,000,000 x 4% + $250,000
= $350,000
Lake Sales had $2,200,000 in sales last month. The contribution margin ratio was 30% and operating profits were $180,000. What is Lake's break-even sales volume
Answer:
$1,600,000
Explanation:
Sales
$2,200,000
Contribution margin ratio
30%
$660,000
Sales $2,200,000
Contribution margin $660,000
Operating profit $180,000
Fixed cost = Contribution margin - Operating profit
= $660,000 - $180,000
= $480,000
Break even sales = Fixed cost / Contribution margin ratio
= $480,000 / 30%
= $1,600,000
Therefore, Lake's break even sales volume is $1,600,000
Suppose you won a $77,000 after-tax cash prize in the lottery. You want to start a new business that you think will lose money for a while, after which it will be up and running and bringing in big bucks. You plan to invest the funds immediately in securities that are expected to earn 8% per year. Suppose you would need only $19,000 per year during the start-up period. How long could you operate before you would require cash from the new business, i.e., how long could you receive payments of $19,000 per year? The first withdrawal will be made a year from today, and your answer will contain a fraction of a year.
Answer:
The right solution is "5.09 years".
Explanation:
The given values are:
Lottery amount
= $77,000
Withdrawal
= $19,000
Rate
= 8%
The number of withdrawal will be:
⇒ [tex]NPER(Rate,-withdrawal,lottery \ amount)[/tex]
On putting the values, we get
⇒ [tex]NPER(8 \ percent,-19000,77000)[/tex]
⇒ [tex]5.09 \ years[/tex]
you can acquire an existing business for $2 million. You are uncertain about future demand. There is a 40% chance of high demand, in which case the present value of the business will be $3 million. There is a 25% chance of moderate demand, and the associated present value is $1.5 million. Finally, there is a 35% chance of low demand, in which case the present value is $1 million. Draw a decision tree for this problem. What is the expected net present value of the business
Answer:
Expected net present value of the project = $1,925,000
Explanation:
The cost of acquiring business = $2,000,000
Expected net present value of the project = High demand NPV*High demand percent + Moderate demand NPV*Moderate demand percent + Low demand NPV*Low demand percent
Expected net present value of the project = $3,000,000 *40% + $1,500,000*25% + $1,000,000*35%
Expected net present value of the project = $1,200,000 + $375,000 + $350,000
Expected net present value of the project = $1,925,000
Conclusion: The cost of acquiring business is more than expected net present value, it is advisable not to invest in the project.
Your grandpa doesn't trust "young 'uns" so you are set to inherit a $1,000,000 trust fund on your 50th birthday. Your Grandpa also doesn't like banks so he has buried the cash somewhere on his 40-acre farm in a location that will be revealed to you by his lawyer since Grandpa will not be around when you turn 50. If you could possibly get your hands on it now (when you are 20), you could put it in a bank at 6% annual interest. If you were able to dig up the money now, how much would you have when you turn 50?
Answer:
FV= $5,743,491.17
Explanation:
Giving the following information:
Present value (PV)= $1,000,000
Number of periods (n)= 30 years
Annual interest= 6% = 0.06
To calculate the future value (FV), we need to use the following formula:
FV= PV*(1+i)^n
FV= 1,000,000*(1.06^30)
FV= $5,743,491.17
4. Give two reasons why GDP is often not seen as the best measure of living standards.
Answer:
Different factors account to it.
Explanation:
Because many factors that contribute to people's happiness are not bought and sold, GDP is a limited tool for measuring standard of living. To understand it's limitations better, let's take a look at several factors that are not accounted for in GDP.
GDP does not account for leisure time. The US GDP per capita is larger than the GDP per capita of Germany, but does this prove that the standard of living in the United States is higher? Not necessarily since it is also true that the average US worker works several hundred hours more per year more than the average German worker. The calculation of GDP does not take German workers extra weeks of vacation into account.
GDP includes what is spent on environmental protection, healthcare, and education, but it does not include actual levels of environmental cleanliness, health, and learning. GDP includes the cost of buying pollution-control equipment, but it does not address whether the air and water are actually cleaner or dirtier. GDP includes spending on medical care, but it does not address whether life expectancy or infant mortality have risen or fallen. Similarly, GDP counts spending on education, but it does not address directly how much of the population can read, write, or do basic mathematics.
Doug and Sue Click file a joint tax return and decide to itemize their deductions. The Clicks' income for the year consists of $89,000 in salary, $1,500 interest income, and $700 long-term capital loss. The Clicks' expenses for the year consist of $1,450 investment interest expense. Assuming that the Clicks' marginal tax rate is 35 percent, what is the amount of their investment interest expense deduction for the year
Answer:
$1,450
Explanation:
Interest Income = $1,500
Investment Interest expenses = $1,450
Allowed deduction limit investment interest is subject to investment income. So $1,450 is allowed as deduction
Farris Corporation, which has only one product, has provided the following data concerning its most recent month of operations: Selling price $ 78 Units in beginning inventory 0 Units produced 8,800 Units sold 8,700 Units in ending inventory 100 Variable costs per unit: Direct materials $ 18 Direct labor $ 10 Variable manufacturing overhead $ 4 Variable selling and administrative expense $ 5 Fixed costs: Fixed manufacturing overhead $255,200 Fixed selling and administrative expense $ 87,000 What is the unit product cost for the month under absorption costing
Answer:
$61
Explanation:
The computation of unit product cost for the month under absorption costing is shown below:-
Unit product cost = Direct material + Direct labor + Variable Manufacturing overhead + Fixed manufacturing cost
= $18 + $10 + $4 + ($255,200 ÷ 8,800)
= $61
Therefore for computing the unit product cost for the month under absorption costing we simply applied the above formula.
A semiannual coupon bond with face value of $1,000 has a coupon rate of 6% and matures in 16 years. The market-determined discount rate on this bond is 14%. What is the price of the bond?
Answer:
$1,125.30
Explanation:
The Price of the Bond is its Current/Trading price also known as the Present Value (PV). This is determined as follows :
Fv = $1,000
Pmt = $1,000 × 6% = $160
P/yr = 1
n = 16
i = 14%
PV = ?
Using the Financial calculator to enter the values as above, the Pv is $1,125.30.
Thus, the price of the bond is $1,125.30.
Dr. Bob Jackson owns a parcel of land that a local farmer has offered to rent from Dr. Bob for the next 10 years. The farmer has offered to pay $20,000 today or an annuity of $3,200 at the end of each of the next 10 years. Which pay-ment method should Dr. Jackson accept if his required rate of return is 10 percent
Answer:
Dr. Jackson should accept the $20,000 paid today
Explanation:
you must analyse the present value of both payment options:
the present value of the $20,000 paid today is exactly $20,000the present value of the annuity = $3,200 x 6.1446 (PV annuity factor, 10%, 10 periods) = $19,662.72Since the present value of the immediate cash payment is higher than the annuity payment, Bob should choose that offer.
A bank offers 8.00% on savings accounts. What is the effective annual rate if interest is compounded semi-annually?Percentage Round to: 4 decimal places (Example: 9.2434%, % sign required. Will accept decimal format rounded to 6 decimal places (ex: 0.092434))
Answer:
Effective Annual Rate = 8.1600%
Explanation:
The effective annual rate the interest rate that is adjusted for compounding over a given period of time. It is given by the formula:
[tex]r = (1+\frac{i}{n})^n -1\\where:\\r = effective\ annual\ rate\\i = nominal\ interest\ rate\ = 8.00\% = 0.08 \\n = number\ of\ compounding\ periods\ per\ year\ = 2\ (semi-annually)[/tex]
[tex]r = (1+\frac{0.08}{2})^2 -1\\r = (1\ +\ 0.04)^2 - 1\\r = (1.04)^2 - 1\\r = 1.0816 - 1\\r = 0.0816\\r = 8.1600 \%[/tex]
The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows. An investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?
Interest Rates
Nominal rate 4.40%
Periodic rate 1.10%
Effective annual rate 4.47%
Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding daily. What is the effective interest rate that Rahul would pay for the loan?
a. 4.081%
b. 4.202%
c. 3.959%
d. 4.395%
Another bank is also offering favorable terms, so Rahul decides to take a loan of $22,000 from this bank. He signs the loan contract at 9% compounded daily for nine months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)
a. $24,477.81
b. $24,948.54
c. $23,536.36
d. $24,007.09
Answer:
1. a. 4.081%
2. c. $23,536.36
Explanation:
1. Periodic rate=(4.4%/4) = 1.1%
EAR=(1+APR/m)^m-1
where m=compounding periods
= (1+0.044/4)^4-1
= 1.011^4 - 1
= 1.04473133864 - 1
= 0.04473133864
= 4.47%
EAR=(1+APR/m)^m-1
where m=compounding periods
=(1+0.04/365)^365-1
= (1+0.00010958904)^365 - 1
= 1.00010958904^365 - 1
= 1.04080849272 - 1
= 0.04080849272
= 4.081%
2. A=P(1+r/365)^365*n
where A=future value, P=present value, r=rate of interest, n=time period.
= 22000*(1+9%/365)^(9/12*365)
= $23,536.36