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Maths 251: Mathematics of Finance Homework 2 - Due at beginning of class on Monday, September 11 Each problem is worth one point. Please show all of your work. You do not have to burn in this question sheet. Express all interest rates as a percent with three decimal places, r.g. 6.051%. All dollar amounts should include cents, Le. two decimal places. I. The nominal interest rate compounded four times per year is " - 85. What is the formula for the accumulation function off) where f is in years? 2. A bank charges a nominal annual rate of interest of 1815 compounded monthly for a cash loan. Calculate the equivalent nominal annual rate of interest All compounded quarterly- 3. A sum of money is deposited into an recount that earns interest at the annual nominal interest rate of 6%% compounded monthly. What is the equivalent annual effective rate of intercu? 4. $1,000 is deposited into an account that carns interest at an annual nominal rate of 6%% compounded monthly. What is the $ amount of interest earned during the first year? 5. $1,000 is invested for three years at the rate of simple interest of 8%% per annum. What nominal rate of interest " compounded twice a year would produce the same ending amount after three years? 6. A bank pays simple interest of 4%% a year on a five-year certificate of deposit. What is the effective rate of interest during the third yearT 7. $2,000 was deposited into an account that earns interest at an annual nominal rate of 6% compounded monthly. Calculate the dollar amount of interest earned during the fifth year. 5. A sum of money was deposited into an account that earned interest at an annual nominal rate of 6%% compounded monthly. How long would it take for the money to double? 9. If $1,000 grows to $3,000 in twelve years, what is the nominal annual rate of interest "* compounded quarterly? 10. John received a nominal annual interest rate of 3% compounded monthly during year one on $10,000 that he had deposited into an account at the beginning of the year. At the beginning of year two John moved his money into a different account that paid a nominal interest rate of 4% compounded weekly. He left the money in the second account for a total of three years. How much money did John have in the account at the end of year four? (The money was in the first account for one year and in the second account for three years.)Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation? 5. In order to better understand how sensitive inequality measures are to the choice of measure, provide a graph of an economy with a 90-10 wage gap that is essentially zero but for which the Gini coefficient is close to 1. Your graph should have "Share of Households" on the x-axis and "Share of Total Income" on the y-axis.6. Suppose there are several perfectly competitive firms producing widgets, and each firm has a production function given by q=10JEW + ED, where Ew and E, are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then MPE JEW + ED . Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each widget is $100. a. Firm A does not discriminate. How many workers of each race would Firm A hire? How much profit does this non-discriminatory firm earn if there are no other costs? b. Firm B discriminates against blacks with a discrimination coefficient of .25. How many workers of each race does this firm hire? How much profit does it earn? c. Firm C has a discrimination coefficient equal to 1.25. How many workers of each race does this firm hire? How much profit does it earn? d. What kind of discrimination are Firms B and C exercising? Taste-based discrimination Statistical discrimination Both taste-based and statistical discrimination iv . Cannot be determinedapproach, they can the nolife redend cheated hid me Michael had hundreds of half-page flyers printed up and hired two kids with bicycles to put one in every mailbox in the neighbourhood: iter CHEAP PAINT JOB FOR YOUR HOUSE Windows, soffits, eaves and downspouts for $350 Here is my phone number: 855-555-3213 Done in one day. Good Work He didn't get a single call. Only slightly discouraged, Michael decided he would have to sell his service by person- ally going door-to-door. He approached each customer with a big smile and his hand ready to shake. "I'm Michael, and I noticed the exterior paint on your house is a real mess," he would begin. When that got no positive responses, Michael began varying his approach: "Hey, how are you? Look, you want a really good paint job for cheap?" Or: "You interested in saving some money on paint work?" At most houses he would be met with a polite refusal (only one slammed door) and the same list of objections to his offer: "Thanks, but my husband (or wife) makes those decisions about the house and he (or she) is away right now." "No, thanks, I do my own repairs and painting around the house." "No, we have our own guy we deal with for that kind of work." "No, I don't mind how it looks. It's not really bad enough to repaint yet." After five days of house-to-house canvassing, Michael only managed to get one cus- tomer. When the work was completed, the customer tried to pay Michael with MasterCard. Michael explained that he only worked for cash, but they finally settled on a personal cheque. Over the next few days, the customer called Michael twice to come back because of "problems" the customer had spotted. In both cases, the problem was related to flaws in the framing or the metal and had nothing to do with Michael's work. Michael was starting to wonder if his business idea was such a good one. 1. Identify any services Michael should be providing other than painting. Explain. 2. Discuss Michael's pricing strategy. Where would you put the price for his service? Why? 3. Critique the advertising piece that Michael is using. Write a better one. 4. Critique the sales approach Michael is using. Suggest alternatives. 5. What sort of signage should Michael use? Explain. 6. How could Michael encourage his one customer (and any future customers) to get referral business for him