Test 1
An investment earns 10% the first year, earns 15% the second year, and loses 12% the third year. The total compound return over the 3 years was ______. A. 41.68% B. 11.32% C. 3.64% D. 13%
B. 11.32% (1.10)(1.15)(1 - .12) - 1 = 11.32%
You have an EAR of 9%. The equivalent APR with continuous compounding is ______. A. 8.47% B. 8.62% C. 8.88% D. 9.42%
B. 8.62% LN[1 + .09] = 8.62%
If you are promised a nominal return of 12% on a 1-year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn? A. 5.48% B. 8.74% C. 9% D. 12%
B. 8.74% Real rate = (1.12/1.03) - 1 = 8.74%
______ is not a derivative security. A. None of the options B. A share of common stock C. A call option D. A futures contract
B. A share of common stock
_______ is not a money market instrument. A. Commercial paper B. A treasury bill C. A treasury bond D. A certificate of deposit
C. A treasury bond
Advantages of investment companies to investors include all but which one of the following? A. Record keeping and administration B. Low-cost diversification C. Professional management D. Guaranteed rates of return
D. Guaranteed rates of return
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 24%, while stock B has a standard deviation of return of 18%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is .0380, the correlation coefficient between the returns on A and B is _________. A. .583 B. .225 C. .327 D. .128
A.
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The expected return on the optimal risky portfolio is _________. A. 14% B. 15.6% C. 16.4% D. 18%
A.
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of return of 20%. Stock B has an expected return of 14% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is .50. The risk-free rate of return is 10%. The proportion of the optimal risky portfolio that should be invested in stock A is _________. A. 0% B. 40% C. 60% D. 100%
A.
Asset A has an expected return of 15% and a reward-to-variability ratio of .4. Asset B has an expected return of 20% and a reward-to-variability ratio of .3. A risk-averse investor would prefer a portfolio using the risk-free asset and ______. A. asset A B. asset B C. no risky asset D. The answer cannot be determined from the data given.
A.
If an investor does not diversify his portfolio and instead puts all of his money in one stock, the appropriate measure of security risk for that investor is the ________. A. stock's standard deviation B. variance of the market C. stock's beta D. covariance with the market index
A.
You sell short 200 shares of Doggie Treats Inc. that are currently selling at $25 per share. You post the 50% margin required on the short sale. If your broker requires a 30% maintenance margin, at what stock price will you get a margin call? (You earn no interest on the funds in your margin account, and the firm does not pay any dividends.) A. $28.85 B. $35.71 C. $31.50 D. $32.25
A. $28.85
The Hydro Index is a price weighted stock index based on the 5 largest boat manufacturers in the nation. The stock prices for the five stocks are $10, $20, $80, $50 and $40. The price of the last stock was just split 2 for 1 and the stock price was halved from $40 to $20. What is the new divisor for a price weighted index? A. 4.50 B. 4.75 C. 5.00 D. 4.85
A. 4.50
Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment? A. 5.14% B. 7.59% C. 9.29% D. 8.43%
A. 5.14%
_____ is an example of an exchange-traded fund. A. An SPDR or spider B. A samurai C. A Vanguard D. An open-end fund
A. An SPDR or spider
According to the Flow of Funds Accounts of the US, the largest asset of U.S. households is A. Real estate B. Mutual fund shares C. Pension reserves D. Corporate equity
A. Real estate
Consider a Treasury bill with a rate following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .0625 The investor must develop a complete portfolio by combining the risk- free asset with one of the securities mentioned above. The security the investor should choose as part of her complete portfolio to achieve the best CAL would be ______. A. Security A B. Security B C. Security C D. Security D
A. Security A A has the steepest slope, found as: Slope = (.15 − .05)/(.04).5 = .5000
Currently, the Dow Jones Industrial Average is computed by _____. A. adding the prices of 30 large "blue-chip" stocks and dividing by a divisor adjusted for stock splits and large stock dividends B. adding the prices of 30 large "blue-chip" stocks and dividing by 30 C. measuring the current total market value of the 30 stocks in the index relative to the total value on the previous day D. calculating the total market value of the 30 firms in the index and dividing by 30
A. adding the prices of 30 large "blue-chip" stocks and dividing by a divisor adjusted for stock splits and large stock dividends
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. A portfolio that has an expected value in 1 year of $1,100 could be formed if you ______. A. place 40% of your money in the risky portfolio and the rest in the risk-free asset B. place 55% of your money in the risky portfolio and the rest in the risk-free asset C. place 60% of your money in the risky portfolio and the rest in the risk-free asset D. place 75% of your money in the risky portfolio and the rest in the risk-free asset
A. place 40% of your money in the risky portfolio and the rest in the risk-free asset $1,100 = y × (1,000)(1.16) + (1 - y)1,000(1.06), so y =.4
Adding additional risky assets to the investment opportunity set will generally move the efficient frontier _____ and to the ______. A. up; right B. up; left C. down; right D. down; left
B.
Diversification is most effective when security returns are _________. A. high B. negatively correlated C. positively correlated D. uncorrelated
B.
Some diversification benefits can be achieved by combining securities in a portfolio as long as the correlation between the securities is _____________. A. 1 B. less than 1 C. between 0 and 1 D. less than or equal to 0
B.
The standard deviation of return on investment A is .10, while the standard deviation of return on investment B is .04. If the correlation coefficient between the returns on A and B is -.50, the covariance of returns on A and B is _________. A. -.0447 B. -.0020 C. .0020 D. .0447
B.
Which of the following statistics cannot be negative? A. Covariance B. Variance C. E(r) D. Correlation coefficient
B.
You short-sell 200 shares of Rock Creek Fly Fishing Co., now selling for $50 per share. If you want to limit your loss to $2,500, you should place a stop-buy order at ____. A. $37.50 B. $62.50 C. $56.25 D. $59.75
B. $62.50 Amount received from short sale = 200 × $50 = $10,000 Loss = $2,500 = 200P - 10,000 $12,500 = 200P, so P = $62.50
Assume that you have just purchased some shares in an investment company reporting $500 million in assets, $50 million in liabilities, and 50 million shares outstanding. What is the net asset value (NAV) of these shares? A. $12 B. $9 C. $10 D. $1
B. $9 NAV = ($500 − $50)/50 = $9
Which of the following are financial assets? I. Debt securities II. Equity securities III. Derivative securities A. I and II only B. I, II, and III C. I only D. II and III only
B. I, II, and III
TIPS are ______. A. securities that trade on the Toronto stock index B. Treasury bonds that protect investors from inflation C. Treasury bonds that pay no interest and are sold at a discount D. U.K. bonds that protect investors from default risk
B. Treasury bonds that protect investors from inflation
Mutual funds that hold both equities and fixed-income securities in relatively stable proportions are called _________. A. income funds B. balanced funds C. asset allocation funds D. index funds
B. balanced funds
The process of polling potential investors regarding their interest in a forthcoming initial public offering (IPO) is called ____. A. interest building B. book building C. market analysis D. customer identification
B. book building
An order to buy or sell a security at the current price is a _______. A. limit order B. market order C. stop-loss order D. stop-buy order
B. market order
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is .4. The risk-free rate of return is 5%. The standard deviation of the returns on the optimal risky portfolio is _________. A. 25.5% B. 22.3% C. 21.4% D. 20.7%
C.
An investor's degree of risk aversion will determine his or her ______. A. optimal risky portfolio B. risk-free rate C. optimal mix of the risk-free asset and risky asset D. capital allocation line
C.
Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return of 10% and a standard deviation of return of 30%. The weight of security B in the minimum- variance portfolio is _________. A. 10% B. 20% C. 40% D. 60%
C.
The _________ reward-to-variability ratio is found on the ________ capital market line. A. lowest; steepest B. highest; flattest C. highest; steepest D. lowest; flattest
C.
The optimal risky portfolio can be identified by finding: I. The minimum-variance point on the efficient frontier II. The maximum-return point on the efficient frontier and the minimum-variance point on the efficient frontier III. The tangency point of the capital market line and the efficient frontier IV. The line with the steepest slope that connects the risk-free rate to the efficient frontier A. I and II only B. II and III only C. III and IV only D. I and IV only
C.
Which one of the following stock return statistics fluctuates the most over time? A. Covariance of returns B. Variance of returns C. Average return D. Correlation coefficient
C.
You find that the annual Sharpe ratio for stock A returns is equal to 1.8. For a 3-year holding period, the Sharpe ratio would equal _______. A. 1.8 B. 2.48 C. 3.12 D. 5.49
C.
You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolios have a correlation of .55. The standard deviation of the resulting portfolio will be ________________. A. more than 18% but less than 24% B. equal to 18% C. more than 12% but less than 18% D. equal to 12%
C.
You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible gain, ignoring transactions cost? A. $50 B. $150 C. $10,000 D. Unlimited
C. $10,000
An investor buys $8,000 worth of a stock priced at $40 per share using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance margin. In 1 year the investor has interest payable and gets a margin call. At the time of the margin call the stock's price must have been ____. A. $20 B. $29.77 C. $30.29 D. $32.45
C. $30.29
Assume you purchased 500 shares of XYZ common stock on margin at $40 per share from your broker. If the initial margin is 60%, the amount you borrowed from the broker is _________. A. $20,000 B. $12,000 C. $8,000 D. $15,000
C. $8,000
The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year? A. -3.64% B. -6.36% C. -6.44% D. -11.74%
C. -6.44% Nominal return on stock: (50 + 3)/55 - 1 = −3.64% Real return: (1 + R) = (1 + r)(1 + i) 1 + r = (1 - .0364)/(1.03) = .935 R = .935 - 1 = -.0644
A portfolio with a 25% standard deviation generated a return of 15% last year when T-bills were paying 4.5%. This portfolio had a Sharpe ratio of ____. A. .22 B. .60 C. .42 D. .25
C. .42
An investor buys $16,000 worth of a stock priced at $20 per share using 60% initial margin. The broker charges 8% on the margin loan and requires a 35% maintenance margin. The stock pays a $.50-per-share dividend in 1 year, and then the stock is sold at $23 per share. What was the investor's rate of return? A. 17.5% B. 19.67% C. 23.83% D. 25.75%
C. 23.83%
You purchased a share of stock for $29. One year later you received $2.25 as dividend and sold the share for $28. Your holding-period return was _____. A. -3.57% B. -3.45% C. 4.31% D. 8.03%
C. 4.31%
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately _____ in the risky portfolio. This will mean you will also invest approximately ______ and _____ of your complete portfolio in security X and Y, respectively. A. 0%; 60%; 40% B. 25%; 45%; 30% C. 40%; 24%; 16% D. 50%; 30%; 20%
C. 40%; 24%; 16%
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. _____ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%. A. 100% B. 90% C. 45% D. 10%
C. 45%
The margin requirement on a stock purchase is 25%. You fully use the margin allowed to purchase 100 shares of MSFT at $25. If the price drops to $22, what is your percentage loss? A. 9% B. 15% C. 48% D. 57%
C. 48%
The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan? A. .50% B. 5% C. 6% D. 6.5%
C. 6% APR = .5% × 12 = 6%
An investor purchases one municipal bond and one corporate bond that pay rates of return of 5% and 6.4%, respectively. If the investor is in the 15% tax bracket, his after-tax rates of return on the municipal and corporate bonds would be, respectively, ______. A. 5.75% and 5.44% B. 4.25% and 6.4% C. 5% and 5.44% D. 5% and 6.4%
C. After-tax return on municipal bond = .05 After-tax return on corporate bond = .064(1 - .15) = .0544 = 5.44%
______ represents an ownership share in a corporation. A. Preferred stock B. A call option C. Common stock D. A fixed-income security
C. Common stock
Which of the following are true statements about T-bills? I. T-bills typically sell in denominations of $10,000. II. Income earned on T-bills is exempt from all federal taxes. III. Income earned on T-bills is exempt from state and local taxes. A. I and II only B. I, II, and III C. I and III only D. I only
C. I and III only
Active trading in markets and competition among securities analysts helps ensure that: I. Security prices approach informational efficiency. II. Riskier securities are priced to offer higher potential returns. III. Investors are unlikely to be able to consistently find under- or overvalued securities. A. I and II only B. II and III only C. I, II, III D. I only
C. I, II, III
Money market securities are characterized by: I. Maturity less than 1 year II. Safety of the principal investment III. Low rates of return A. I and II only B. I only C. I, II, III D. I and III only
C. I, II, III
______ funds stand ready to redeem or issue shares at their net asset value. A. Closed-end B. Index C. Open-end D. Hedge
C. Open-end
______ assets generate net income to the economy, and _____ assets define allocation of income among investors. A. Real, real B. Financial, financial C. Real, financial D. Financial, real
C. Real, financial
You decide to purchase an equal number of shares of stocks of firms to create a portfolio. If you wanted to construct an index to track your portfolio performance, your best match for your portfolio would be to construct _____. A. a bond price index B. a value-weighted index C. a price-weighted index D. an equally weighted index
C. a price-weighted index
You have calculated the historical dollar-weighted return, annual geometric average return, and annual arithmetic average return. If you desire to forecast performance for next year, the best forecast will be given by the ________. A. dollar-weighted return B. geometric average return C. arithmetic average return D. index return
C. arithmetic average return
The ratio of trading activity of a portfolio to the assets of the portfolio is called the _____. A. reinvestment ratio B. trading rate C. portfolio turnover D. tax yield
C. portfolio turnover
Investors who want to liquidate their holdings in a closed-end fund may ______. A. sell their shares back to the fund at a discount if they wish B. sell their shares back to the fund at net asset value C. sell their shares on the open market D. sell their shares at a premium to net asset value if they wish
C. sell their shares on the open market
If an investor places a _________ order, the stock will be sold if its price falls to the stipulated level. If an investor places a __________ order, the stock will be bought if its price rises above the stipulated level. A. stop-buy; stop-loss B. market; limit C. stop-loss; stop-buy D. limit; market
C. stop-loss; stop-buy
Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return, and a 30% chance of losing 6%. What is your expected return on this investment? A. 12.8% B. 11% C. 8.9% D. 9.2%
D. 9.2% (.2)(30%) + (.5)(10%) + (.3)(-6%) = 9.2%
Which of the following is not a financial intermediary? A. An insurance company B. A credit union C. A mutual fund D. A real estate brokerage firm
D. A real estate brokerage firm
The Dodd-Frank Reform act does all of the following except: A. Reduces capital requirements for banks B. Requires public companies to set "claw-back" provisions C. Creates an office within the SEC to oversee credit rating agencies D. Increases transparency in the derivatives market E. Limits the risk-taking in which banks can engage
A. Reduces capital requirements for banks
A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 shares, and 553,000 shares, respectively. If the market value weighted index was 970 yesterday and the prices changed to $23, $41, and $58 today, what is the new index value? A. 985 B. 975 C. 960 D. 970
B. 975
Which of the following is not a true statement regarding municipal bonds? A. The interest income from a municipal bond is exempt from state and local taxation in the issuing state. B. A municipal bond is a debt obligation issued by the federal government. C. A municipal bond is a debt obligation by state or local governments. D. The interest income from a municipal bond is exempt from federal income taxation.
B. A municipal bond is a debt obligation issued by the federal government.
The systematic risk that led to the financial crisis of 2008 was increased by _____. A. Collateralized debt obligations B. All of the options C. Credit default swaps D. Subprime mortgages
B. All of the options
The Wildwood Fund sells Class A shares with a front-end load of 5% and Class B shares with a 12b-1 fee of 1% annually. If you plan to sell the fund after 4 years, are Class A or Class B shares the better choice? Assume a 10% annual return net of expenses before the 12b-1 fee is applied. A. Class A. B. Class B. C. There is no difference. D. The answer cannot be determined from the information given.
B. Class B.
Which of the following is not a characteristic of a money market instrument? A. Low risk B. Maturity greater than 1 year C. Marketability D. Liquidity
B. Maturity greater than 1 year
You are considering investing in one of several mutual funds. All the funds under consideration have various combinations of front-end and back-end loads and/or 12b-1 fees. The longer you plan on remaining in the fund you choose, the more likely you will prefer a fund with a __________ rather than a __________, everything else equal. A. 12b-1 fee; front-end load B. front-end load; 12b-1 fee C. back-end load; front-end load D. 12b-1 fee; back-end load
B. front-end load; 12b-1 fee
Preferred stock is like long-term debt in that ______. A. the preferred dividend is a tax-deductible expense for the firm B. it promises to pay to its holder a fixed stream of income each year C. in the event of bankruptcy preferred stock has equal status with debt D. it gives the holder voting power regarding the firm's management
B. it promises to pay to its holder a fixed stream of income each year
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. The slope of the capital allocation line formed with the risky asset and the risk-free asset is approximately _____. A. 1.040 B. .80 C. .50 D. .25
C. .50 Slope = (16 - 6)/20 = .50
The historical average rate of return on large company stocks since 1926 has been _____ A. 8% B. 20% C. 11.5% D. 5%
C. 11.5%
An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5%, and she puts 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are __________ and __________ respectively. A. 10%; 6.7% B. 12%; 22.4% C. 12%; 15.7% D. 10%; 35%
C. 12%; 15.7%
Under SEC rules, the managers of certain funds are allowed to deduct charges for advertising, brokerage commissions, and other sales expenses directly from the fund assets rather than billing investors. These fees are known as ______. A. direct operating expenses B. back-end loads C. 12b-1 charges D. front-end loads
C. 12b-1 charges
Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in 6 months. What is the effective annual rate of return for this investment? A. 6.38% B. 12.77% C. 13.17% D. 14.25%
C. 13.17%
The geometric average of -12%, 20%, and 25% is ______. A. 8.42% B. 11% C. 9.7% D. 18.88%
C. 9.7% [(1 + −.12)(1 + .20)(1 + .25)]^(1/3) - 1 = 9.70%
Rank the following from highest average historical return to lowest average historical return from 1926 to 2010. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills A. I, II, III, IV B. III, IV, II, I C. I, III, II, IV D. III, I, II, IV
C. I, III, II, IV
Initial public offerings (IPOs) are usually ___________ relative to the levels at which their prices stabilize after they begin trading in the secondary market. A. overpriced B. correctly priced C. underpriced D. mispriced, but without any particular bias
C. underpriced
Financial markets allow for all but which of the following? A. Channel funds from lenders of funds to borrowers of funds B. Shift consumption through time from higher-income periods to lower C. Price securities according to their riskiness D. Allow most participants to routinely earn high returns with low risk
D. Allow most participants to routinely earn high returns with low risk
Real assets include all but which of the following A. Buildings B. Land C. Consumer durables D. Common stock
D. Common stock
Higher portfolio turnover: I. Results in greater tax liability for investors II. Results in greater trading costs for the fund, which investors have to pay for III. Is a characteristic of asset allocation funds A. I only B. II only C. I and II only D. I, II, and III
D. I, II, and III
The cost of buying and selling a stock includes: I. Broker's commissions II. Dealer's bid-asked spread III. Price concessions that investors may be forced to make A. I and II only B. II and III only C. I and III only D. I, II, and III
D. I, II, and III
The Sarbanes-Oxley Act corporate governance rules by requiring all but which one of the following? A. Required that corporations have more independent directors. B. Required that the CFO personally vouch for the corporation's financial statements. C. Required the creation of a new board to oversee the auditing of public companies. D. Required that firms could no longer employ investment bankers to sell securities to the public.
D. Required that firms could no longer employ investment bankers to sell securities to the public.
_____ often accompany short sales and are used to limit potential losses from the short position. A. Limit orders B. Restricted orders C. Limit loss orders D. Stop-buy orders
D. Stop-buy orders
Which one of the following would be considered a risk-free asset in real terms as opposed to nominal? A. Money market fund B. U.S. T-bill C. Short-term corporate bonds D. U.S. T-bill whose return was indexed to inflation
D. U.S. T-bill whose return was indexed to inflation
You short-sell 200 shares of Tuckerton Trading Co., now selling for $50 per share. What is your maximum possible loss? A. $50 B. $150 C. $10,000 D. Unlimited
D. Unlimited
You have $500,000 available to invest. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should ______. A. invest $125,000 in the risk-free asset B. invest $375,000 in the risk-free asset C. borrow $125,000 D. borrow $375,000
D. borrow $375,000 y × .16 + (1 - y) × .08 = .22 .16 y - .08 y + .08 = .22 .08 y = .14 y = 1.75 Put 1.75 × $500,000 = $875,000 in the risky asset by borrowing $375,000.
According to multiple studies by Ritter, initial public offerings tend to exhibit __________ performance initially and __________ performance over the long term. A. bad; good B. bad; bad C. good; good D. good; bad
D. good; bad
Specialized-sector funds concentrate their investments in _________. A. bonds of a particular maturity B. geographic segments of the real estate market C. government securities D. securities issued by firms in a particular industry
D. securities issued by firms in a particular industry
You purchased XYZ stock at $50 per share. The stock is currently selling at $65. Your gains could be protected by placing a _____. A. limit buy order B. limit sell order C. market order D. stop-loss order
D. stop-loss order
In a _____ index, changes in the value of the stock with the greatest market value will move the index value the most, everything else equal. A. equally weighted index B. price-weighted index C. bond price index D. value-weighted index
D. value-weighted index
A T-bill quote sheet has 90-day T-bill quotes with a 4.92% bank discount rate (in other words 4.92 bid). If the bill has a $10,000 face value, an investor could buy this bill for _____.
Equation... number 4 part 2