The value of a stock increases by 4% every year. At the beginning of February 1st, 2020 it is valued at 30 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, 2020. V = 30(1.04)^^t (b) What is the value of the stock at the beginning of February 1st, 2027? Value: 39.478 dollars (c) How quickly is the value of the stock increasing at the beginning of February 1st, 2027? Rate: 1.55 dollars per year (d) What is the continuous growth rate of V? That is, if the stock is growing like continuously compounded interest, what growth rate would give 4% growth per year? Rate: 0.03922 per year (e) What is the percentage rate of change in the value of the stock at the beginning of February 1st, 2027? Percentage rate: % per year (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 the continuous growth rate in particular.

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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The value of a stock increases by 4% every year. At the beginning of February 1st, 2020 it is valued at 30 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, 2020.
V =
30(1.04)^t
(b) What is the value of the stock at the beginning of February 1st, 2027?
Value: 39.478
dollars
(c) How quickly is the value of the stock increasing at the beginning of February 1st, 2027?
Rate:
1.55
dollars per year
(d) What is the continuous growth rate of V? That is, if the stock is growing like continuously compounded interest, what growth rate would
give 4% growth per year?
Rate: 0.03922
per year
(e) What is the percentage rate of change in the value of the stock at the beginning of February 1st, 2027?
Percentage rate:
% per year
(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 the continuous growth rate in particular.
Transcribed Image Text:The value of a stock increases by 4% every year. At the beginning of February 1st, 2020 it is valued at 30 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, 2020. V = 30(1.04)^t (b) What is the value of the stock at the beginning of February 1st, 2027? Value: 39.478 dollars (c) How quickly is the value of the stock increasing at the beginning of February 1st, 2027? Rate: 1.55 dollars per year (d) What is the continuous growth rate of V? That is, if the stock is growing like continuously compounded interest, what growth rate would give 4% growth per year? Rate: 0.03922 per year (e) What is the percentage rate of change in the value of the stock at the beginning of February 1st, 2027? Percentage rate: % per year (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 the continuous growth rate in particular.
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