Suppose there are only 2 investment alternatives: a bank deposit that pays 4% per year and a 2-year coupon bond with 5% annual coupon rate and face value of $1,000. Assume the bank deposit and coupon bond are perfect substitutes. a) What is the market price of the bond at beginning of year 1? And year 2? b) Assume now that at the beginning of year 2, the deposit interest rate unexpectedly increases to 6% annual. What is the market price of the bond at the beginning of year 2? What is the yearly return on the bond in each year?

Find the curvature of the parametrized curve ~r(t) =< 2t 2 , 4 + t, −t 2 >.

Use the equation given to solve the following problems:

2 KMnO ₄ + 16 HCl —> 5 Cl ₂ + 2 KCl + 2 MnCl ₂ + 8 H₂O

(a) How many moles of HCl are required to react with 35.0 g of KMnO₄ ?

(b) How many grams of Cl₂ will be produced from 3.50 mol of KMnO₄ ?

(c) To produce 50.0 g of MnCl₂ , how many mL of 3.00 M HCl will react?

(d) What is the maximum mass of Cl₂ that can be produced by recting 25.0 g of KMnO₄   with 50.00 mL of 2.00 M HCl?

4. A Rankine cylce operates between pressures of 2 psia and 1500 psia. If the steam entering the turbine is superheated to 800^oF, calculate the efficiency of the cycle. Neglect pump work. Note: The peak of the superheat phase of this cycle is outside the range of the text steam tables and is difficult to locate on the text Mollier chart since it does not have a 1500 psia constant pressure line. Please use the following information taken from the Combustion Engineering steam tables. At 1500 psia and 800 ^oF, the steam would have an h = 1364 Btu/lbm and an s = 1.5073 Btu/lbm ^oR. You should be able to find the value of h at 2 psia and an s = 1.5073 Btu/lbm ^oR from the text steam tables or the Mollier chart. Then you can calculate the parameters requested by questions 4 and 5.

State your answer as a percent to one decimal place. Example: 35.2

5. A Rankine cycle operates between pressures of 2 psia and 1500 psia. If the steam entering the turbine is superheated to 800^oF, calculate the work produced per pound mass of steam. Neglect pump work.

State your answer to two decimal places. Example:125.25

I WILL RATE YOU

Question 2

Graph P(X=x) for binomial distributions with the following parameters
a) ? = 4 ??? ? = 0.5
b) ? = 4 ??? ? = 0.3
c) ? = 4 ??? ? = 0.1
d) Which if any of the graphs in part a-c are symmetric?
e) Without actually constructing the graph, would the case
? = 10 ??? ? = 0.5 be symmetric or skewed?
f) Which of the graphs in part a-c is the most heavily skewed?
g) Without actually constructing the graph, would the case ? = 4 and
? = 0.01 exhibit more or less skewness than the graph in part(c)?

Question 3

Suppose that a random variable y has a Poisson distribution.
Compute the following probabilities
a) P(y = 4) given ? = 3
b) P(y<4) given ? = 3
c) P(y<=4) given ? = 3
d) P(y>4) given ? = 3
e) P(2<y<5) given ? = 3

Question 4

The number of calls coming to the customer care center of a mobile company per
minute is a Poisson random variable with mean 5. Find the probability that no call
comes in a certain minute

P. 4-2 For each of the following indicate the amount of revenue that Beanville should recognize in its 2017 (1) government-wide statements and (2) governmental fund statements. Provide a brief justification or explanation for your responses. The state in which Beanville is located collects sales taxes for its cities and other local governments. The state permits small merchants to remit sales taxes quarterly. The state sales tax rate is 6 percent. In December 2016, city merchants collected $50 million in sales taxes that they remitted to the state on January 15, 2017. The state, in turn, transferred the taxes to the city on February 15, 2017. In December 2016, the federal government awarded Beanville a reimbursement grant of $500,000 to train law-enforcement agents. The city had applied for the grant in January of that year. The city may incur allowable costs any time after receiving notification of the award. In 2017, the city incurred $400,000 in allowable costs and was reimbursed for $350,000. It was reimbursed for the $50,000 balance in February 2018. In January and February 2018, it incurred the remaining $100,000 in allowable costs and was reimbursed for them in April 2018. In December 2016 the city levied property taxes of $1 billion for the calendar year 2017. The taxes are due June 30, 2017. The city collected these taxes as follows: December 2016 $ 56 million January 1, 2016, to December 31, 2016 $ 858 million January 1, 2017, through March 31, 2017 ($18 million per month) $ 54 million Total $ 968 million It estimates the balance of $32 million would be uncollectible. In addition, in the period from January 1 through February 28, 2017, the city collected $16 million in taxes that were delinquent as of December 31, 2016. In the period March 1 through June 30 2017, the city collected $8 million of taxes that were also delinquent as of December 31, 2016. In December 2017 Beanville sold a city-owned warehouse to a private developer. Sales price was $4.2 million. The warehouse had cost $4 million when it was acquired 10 years earlier. It had an estimated useful life of 40 years (with no salvage value). In December 2017, Beanville's city-owned radio station held its annual fund drive. A local business offered to match all pledges made on December 2, 2017, up to $50,000, assuming that the amount pledged was actually collected. Based on past experience the city estimates that 90 percent of the pledges will actually be collected. By year-end 2017, the city had collected $25,000 of the pledges, and in January and February it collected an additional $15,000. It received $25,000 of the matching funds on February 15, 2018. Respond with respect only to the $50,000 in matching funds.

P. 4-2

For each of the following indicate the amount of revenue that Beanville should recognize in its 2020 (1) government‐wide statements and (2) governmental fund statements. Provide a brief justification or explanation for your responses.

1. The state in which Beanville is located collects sales taxes for its cities and other local governments. The state permits small merchants to remit sales taxes quarterly. The state sales tax rate is 6 percent. In December 2019, city merchants collected $50 million in sales taxes that they remitted to the state on January 15, 2020. The state, in turn, transferred the taxes to the city on February 15, 2020.
2. In December 2019, the federal government awarded Beanville a reimbursement grant of $500,000 to train law‐enforcement agents. The city had applied for the grant in January of that year. The city may incur allowable costs any time after receiving notification of the award. In 2020, the city incurred $400,000 in allowable costs and was reimbursed for $350,000. It was reimbursed for the $50,000 balance in February 2021. In January and February 2021, it incurred the remaining $100,000 in allowable costs and was reimbursed for them in April 2021.
3. In December 2019, the city levied property taxes of $1 billion for the calendar year 2020. The taxes are due on June 30, 2020. The city collected these taxes as follows:

December 2019                                                                                                                                 $56 million

January 1, 2019, to December 31, 2019    $858 million

January 1, 2020, through March 31, 2020 ($18 million per month) $54 million

Total                                                                                                                                                    $968 million

It estimates the balance of $32 million would be uncollectible. In addition, in the period from January 1 through February 28, 2020, the city collected $16 million in taxes that were delinquent as of December 31, 2019. In the period March 1 through June 30 2020, the city collected $8 million of taxes that were also delinquent as of December 31, 2019.

4. In December 2020 Beanville sold a city‐owned warehouse to a private developer. Sales price was $4.2 million. The warehouse had cost $4 million when it was acquired 10 years earlier. It had an estimated useful life of 40 years (with no salvage value).
5. In December 2020, Beanville's city‐owned radio station held its annual fund drive. A local business offered to match all pledges made on December 2, 2020, up to $50,000, assuming that the amount pledged was actually collected. Based on past experience the city estimates that 90 percent of the pledges will actually be collected. By year‐end 2020, the city had collected $25,000 of the pledges, and in January and February it collected an additional $15,000. It received $25,000 of the matching funds on February 15, 2021. Respond with respect only to the $50,000 in matching funds.

If the time to failure distribution (PDF) is given by f(t) = gt^-4 (t > 2) and f(t) = 0 for t ? 2:

a) What is the value of g?

b) What is the mean time to failure?

c) What is the instantaneous failure rate?

Steve and Rebecca have 2 small children ages 3 and 4. They have moved to the suburbs and bought a house to provide enough space for their kids to run around and burn energy so that they have time to binge watch their TV shows. They have a sizable mortgage of $720,000 on the home. They earn a combined take home salary of $225,000. They want their kids to pursue post-secondary education but don’t expect either of the children will get a scholarship, so they need to save up $100,000. Their best friend is a financial planner and helped them finance a new SUV. The monthly loan payments are $125. Even with their large salary they are worried about their ability to repay the car loan, save for their kids’ education and have the mortgage paid off by retirement, which is 27 years away. It seems like a long time, but monthly income just seems to disappear, and their debts don’t! They have the following investment portfolios:

Joint bank account

9,200

Steve Non-registered account

150 shares of BCE

9450

Rebecca TFSA

High interest Savings

1200

Non-redeemable GIC 25SEP2022 maturity – 1.75%

3000

Total TFSA = 4,200

Steve RRSP

Canadian Balanced ETF

15150

US Equity ETF

28650

Canadian Income Fund

50000

Total RRSP = 93,800

Rebecca RRSP

Cash

500

Cashable GIC maturing 25DEC2020

5000

High Yield Fixed Income

15000

Global balanced

12580

Canadian short-term fixed income

22569

Canadian fixed income

15789

Total RRSP = 71,438

Family RESP Account

Cash

200

What is their investment goal?

What is type of investment account do we recommend?

Asset allocation of the portfolio and why this is appropriate

Other aspects you need to consider that are not specifically noted