The value of a stock increases by 5% every month. At the beginning of February 1

Question

The value of a stock increases by 5% every month. At the beginning of February 1st, 2012 it is valued at 70 dollars per share.

(a) Write a formula for the value of the stock (in dollars) as a function of time, t, in years after the beginning of February 1st, 2012.

(b) What is the value of the stock at the beginning of February 1st, 2018?

(c) How quickly is the value of the stock increasing at the beginning of February 1st, 2018?

(d) What is the continuous growth rate of V?

(e) What is the percentage rate of change in the value of the stock at the beginning of February 1st, 2018?

(Compare this to your answer in part (d). Remember that this characteristic is the defining one for an exponential function, and it is why we care about thecontinuousgrowth rate in particular.

Explanation / Answer

a) Value of stock = Price at Feb 1, 2012 * (1 + i)^t

b) Value of the stock at the beginning of February 1st, 2018 = 70 * (1 + .05)^72 = 2348.16

c) Stock increasing rate at the beginning of February 1st, 2018 = (P1/P0)^1/n - 1

= (2348.16 / 70)^(1 / 6) - 1

= 79.59% (Annual increase rate)

d) Continuous growth rate = 1*2.7182818^(.05*12) = 182.21%

e) % change in value of stock = (2348.16 - 70) / 70 = 3254.51%

% change annual rate = 3254.51% / 6 = 542.42%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.