17. The terminal value of an investment for T years at an annually compounded rate, r is given by wwwwwwww VT = P[1 + (1+r)+(1+r)²+...+(1+r)T-1]. What is the value of VT in terms of P, r and T. www P((1+r)T-1) (1+Pr)T-1) В. А. r r - 1 (P(1+r)T-1-1) В. P((1+r)T-1) D. r - 1 r - 1 O A. A О В. В ОС. С O D. D
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![17. The terminal value of an investment for T years at an
annually compounded rate, r is given by
VT = P[1+ (1+r)+(1+r)²+...+(1+r)T-1].
What is the value of VT in terms of P, r and T.
P((1+r)"-1)
А.
(1+Pr)T-1)
В.
r
r - 1
(P(1+r)™-1–1)
P(1+r)T-1)
В.
D.
r - 1
r - 1
O A. A
В. В
С. С
O D. D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd615f9d2-7ef4-4124-85aa-f7fcb706a4be%2Fe27ef9ce-5ff1-477a-ab5b-cf2cbfd2ef30%2Fzrl12l7_processed.jpeg&w=3840&q=75)
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- Assume S = $45, σ = 0.25, r = 0.05, div = 0.0, on a 45 strike call and 55 days until expiration. Given delta = 0.5502 and gamma = 0.0876, what is the delta-gamma approximation for the call price on a $0.90 stock price decline?3. Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams initially, and after 10 years, 0.6% of the original amount decomposed, design an equation that will represent the amount of remaining element at any given time.At time t = 0, there is one individual alive in a certain population. A pure birth process then unfolds as follows. The time until the first birth is exponentially distributed with parameter λ. After the first birth, there are two individuals alive. The time until the first gives birth again is exponential with parameter λ, and similarly for the second individual. Therefore, the time until the next birth is the minimum of two exponential (λ) variables, which is exponential with parameter 2λ. Similarly, once the second birth has occurred, there are three individuals alive, so the time until the next birth is an exponential rv with parameter 3λ, and so on (the memoryless property of the exponential distribution is being used here). Suppose the process is observed until the sixth birth has occurred and the successive birth times are 25.8, 42.0, 52.0, 55.8, 59.2, 63.3 (from which you should calculate the times between successive births). Derive the mle of λ. [Hint: the likelihood is a…
- Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnYIt is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. Find the projected population after 24 hours for the following conditions.(a) No antibiotic is present, so the relative growth rate is 12%.(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.The work force of a certain factory is growing at rate of 2 per month while the average productivity of a worker is growing at a rate of 4 units per month. If the work force is currently 100 and the average productivity per month is 200 units, at what rate is the total productivity per month of the factory increasing?
- Please answer this question using the assumptions from the Solow Model In a country, the production function in terms of output per capita, y, and capital per labor, k, is y = k(12) The fraction of output saved, s, is 25% and the depreciation rate, δ, is 0.05. Assume that the population does not grow. What is the steady-state of capital per worker, k*, and output per worker, y*? What happens to the steady-state values if the population growth rate rises to 5%? By how much would the country have to increase its savings rate in b) in order to reach the same levels of steady-state values as in a)? Does the country’s growth rate increase in c) compared to a)? how?Overtaking City A has a current population of 500,000 people and grows at a rate of 3%/yr. City B has a current population of 300,000 and grows at a rate of 5%/yr.a. When will the cities have the same population?b. Suppose City C has a current population of y0 < 500,000 and a growth rate of p > 3%/yr. What is the relationship between y0 and p such that Cities A and C have the same population in 10 years?Suppose a man is 30 years old and would like to retire at age 60. Furthermore, he would like to have a retirement fund from which he can draw an income of $75,000 per year—- forever. How can he do it? Assume a constant APR of 6%. He can have a retirement fund from which he can draw $75,000 per year by having $? in his savings account when he retires.