Simple and compound interest, proportions, ratios, annuities,break-even analysis. math homework help

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Wryran

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Question 1 A manufacturer sells a product for $10 inclusive of a government tax. Due to cost pressures, the company increases the price by 15 percent. Some time later the government reduces the tax on this product, bringing the price down by 15 percent. Is the price of the product once again $10? Show calculations that support your answer. Question 2 A company operates a savings scheme for its employees, with interest at 5.6% per year compounded monthly. (a) Calculate the amount saved at the end of 5 years when $200 is deposited at the end of each month. (b) How much should be saved from a monthly salary in order to have $15,000 at the end of 5 years? Question 3 Classic Furniture advertises a “One-Year No-Interest Sale” on any purchase over $499. They require a deposit of 10%, with the balance of the purchase price to be paid in 12 equal monthly payments with no interest charged. (a) What is the cash price equivalent to Classic’s no-interest plan on an item ticketed at $1,000? Assume an interest rate of 11.5% per year compounded monthly. Is this a good deal for a customer? Give a reason. (b) Flemmings Furniture offers the same no interest plan but requires an establishment fee of $25 payable immediately. Flemmings also charges an account keeping fee of $3.95 per month due with each payment. What is the cash price equivalent to Flemmings’ no-interest plan on an item ticketed at $1,000? Assume the same interest rate as in part (a). Is this a good deal for a customer? Give a reason. Question 4 Air Atlantic is considering a new service between two cities. Its existing planes, each of which has a capacity of carrying 240 passengers, could be used for one flight a week with fixed costs of $30,000 and variable costs amounting to 50% of the ticket price. (a) Air Atlantic is thinking of charging $200 per ticket. How many passengers will the airline need on each flight to break even? Find the break-even point algebraically and by using an EXCEL graph. Attach the printout or copy your EXCEL graph into your assignment submission. EXCEL Instructions: Create a column called Number of Passengers and in that column enter values from 0 to 400 in increments of 20. Then create two more columns, one for Total Cost and another for Total Revenue. Enter appropriate formulae in EXCEL to obtain the total cost and total revenue corresponding to each value in the Number of Passengers column. Highlight the resulting three sets of numbers and go to the Insert tab (or Chart menu) to obtain an appropriate diagram. Make sure that your graph has been labelled appropriately (i.e. title, axis labels, legend). Please refer to Topic 3 in the EXCEL Booklet for further instructions on entering formulae and graphing in EXCEL. (b) Based on your analysis from part (a), and without any additional calculations, will Air Atlantic realize a profit or a loss if 240 seats are sold for a flight? Does the break-even number of passengers from part (a) seem reasonable? Explain briefly. (c) What price per seat should Air Atlantic charge to break-even on a full flight? Find the break-even ticket price algebraically Mathematical Formulae 1. Simple interest (I ) is: I =P ×R×T 2. The maturity value (M ) of the principal is: M = P +I M = P (1 + R × T ) 3. The amount of principal (P ) required is: P = M 1+R×T 4. The compound interest formula for the accumulated value (M ) is: M = P (1 + i)n 5. The present value (P ) at compound interest of an amount M is: P = M (1 + i)−n 6. The compound interest rate (i ) per period is:  i= M P  n1 −1 7. The number of periods (n) required for an amount of P to accumulate to an amount of M, when the compound interest rate is i per period, is:   M log P n= log(1 + i) 8. The future value (S ) of annuity is: S =R× (1 + i)n − 1 i 9. The present value (A) of annuity is: 1 − (1 + i)−n A=R× i   10. The amount of the annuity payment (R) made per period is: R= S (1 + i)n − 1 i 11. The amount of the annuity payment (R) made per period is: R= A 1 − (1 + i)−n i 12. Net profit (P ) is: P = Income – Cost = I − C 13. The total cost (C ) is: C = Variable cost + Fixed Cost 14. Break-even volume (x ) is: x= f s−v 15. Net profit (P ) is: P = I − C = sx − (f + vx) = (s − v)x − f Statistical Formulae 1. The arithmetic mean (x̄) of a set of n observations is: P x̄ = x n 2. If each x-value in a set of observations is assigned a corresponding weight (w ), the weighted arithmetic mean is: P xw x̄ = P w 3. Range = largest observation - smallest observation 4. Interquartile range = Q3 – Q1 5. A standard score is defined as: Standard score = z = observed value – mean standard deviation 6. The standard score (z ) of an observation x from a population with mean µ and standard deviation σ is: z= x−µ σ 7. To convert a standard score z to a raw score x, for a distribution with mean µ and standard deviation σ use: x = µ + zσ 8. To convert a mean of x̄ to a z -score use: z= x̄ − µ σ √ n 9. If σ is known: σ Standard error of the mean = √ n 10. If σ is unknown and n is large: s Standard error of the mean = √ n 11. If σ is known and the population is Normal, a confidence interval for µ is:   σ σ x̄ − z √ , x̄ + z √ n n 12. If σ is known, n is large, but the population distribution is unknown or not Normal, a confidence interval for µ is:   σ σ x̄ − z √ , x̄ + z √ n n 13. If σ is unknown and n is large, a confidence interval for µ is:   s s x̄ − z √ , x̄ + z √ n n 14. The sample size required for a specified confidence z and error e n≥ z2σ2 e2 Use s if σ is unknown. 15. Common z values are: For a 90% interval, use z = 1.645 For a 95% interval, use z = 1.96 For a 99% interval, use z = 2.58 16. The formula for a one-sample z -test statistic where σ is known is: z= x̄ − µ0 σ √ n 17. The formula for a one-sample z -test statistic where σ is unknown and n is large is: z= x̄ − µ0 s √ n 18. The population least-squares regression line is denoted by: ŷ = α + βx where α and β are constants 19. The sample least-squares regression line is denoted by: ŷ = a + bx where a and b are constants
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Chart Title
Profit
(30.000)
(28.000)
(26.000)
(24.000)
(22.000)
(20.000)
(18.000)
(16.000)
(14.000)
(12.000)
(10.000)
(8.000)
(6.000)
(4.000)
(2.000)
2.000
4.000
6.000
8.000
10.000

100.000
80.000
60.000

Dollars

Number of
Total
Passenders Total Cost Revenue
30.000
20
32.000
4.000
40
34.000
8.000
60
36.000
12.000
80
38.000
16.000
100
40.000
20.000
120
42.000
24.000
140
44.000
28.000
160
46.000
32.000
180
48.000
36.000
200
50.000
40.000
220
52.000
44.000
240
54.000
48.000
260
56.000
52.000
280
58.000
56.000
300
60.000
60.000
320
62.000
64.000
340
64.000
68.000
360
66.000
72.000
380
68.000
76.000
400
70.000
80.000

40.000
20.000
(20.000)

- 20 40 60 80
100 120 140160 180

(40.000)

Number of Passengers
Total Cost

Total Revenue

Chart Title

160180 200 220 240260 280 300 320340 360 380 400

Number of Passengers
Total Revenue

Profit


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Math Questions
Question 1
A manufacturer sells a product for $10 inclusive of a government tax. Due to cost
pressures, the company increases the price by 15 percent. Some time later the
government reduces the tax on this product, bringing the price down by 15 percent. Is
the price o...


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