a. Invest all $15,000 in the stock, buying 100 shares. b. Invest all $15,000 in 1,500 options (15 contracts). c. Buy 100 options
(one contract) for $1,000, and invest the remaining $14,000 in a money market fund paying 5% in interest over 6 months (10% per year). What is your rate of return for each alternative for the following four stock prices in 6 months? (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round the "Percentage return of your portfolio (Bills + 100 options)" answers to 2 decimal places.)
1 answer:
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Answer: The change in revenue for the sale of 1 more doghouse $ 66.67 dollars
Explanation: Differential is a function that can be used to approximate function value with a great degree of accuracy. This is done by the following.
Mathematical definition of derivative: f'(x) = lim f(x+Δx) - f(x)/Δx.
If Δx is very small:
f'(x) . Δx ≅ f(x+Δx) - f(x)
Knowing that Δy ≅ f(x+Δx) - f(x) and the diferential of variable x can be written by dx as the variable y can be dy:
dy = f'(x) dx
which means that the differential dy is approximately equal to the change Δy, if Δx is very small.
For the question, R(x) = y(x) = 14,000ln(0.01x+1)
f'(x) =
Using the chain rule, the derivative will be:
f'(x) = 14,000.
dy = 14,000..dx
dx is the change in x. For the question, the change is 1 (1 more doghouse) and x is 110:
dy = 14,000
dy =
dy = 66.67
The change in revenue is $66.67 dollars.