The value of a bank account collecting interest which is continuously compounded is modeled by the equation: A = Pet where: A is the value of the account at time t P, or the principal, is the value of the initial investment t is time (measured in years) r is the interest rate (written as a decimal) 1. Suppose that $5000 is put into an account with an interest rate of 8% compounded continuously. a) How much will the account be worth after 3 years (exact value) ? b) How much will the account be worth after 3 years (rounded to the nearest cent) ? c) How many years will it take for the value of the account to double?
The value of a bank account collecting interest which is continuously compounded is modeled by the equation: A = Pet where: A is the value of the account at time t P, or the principal, is the value of the initial investment t is time (measured in years) r is the interest rate (written as a decimal) 1. Suppose that $5000 is put into an account with an interest rate of 8% compounded continuously. a) How much will the account be worth after 3 years (exact value) ? b) How much will the account be worth after 3 years (rounded to the nearest cent) ? c) How many years will it take for the value of the account to double?
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
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:The value of a bank account collecting interest which is continuously compounded is
modeled by the equation: A = Pet where:
A is the value of the account at time t
P, or the principal, is the value of the initial investment
t is time (measured in years)
r is the interest rate (written as a decimal)
1. Suppose that $5000 is put into an account with an interest rate of 8% compounded
continuously.
a) How much will the account be worth after 3 years (exact value) ?
b) How much will the account be worth after 3 years (rounded to the nearest cent) ?
c) How many years will it take for the value of the account to double?
In an exponential model for population growth, the size of a population at time t is
rt
described by the equation: N(t) = Net where:
N is the initial population or the population at t=0
r is the percentage growth rate
t = time and can be measured in different units depending on the problem.
Note: You don't have to use e and r. It is often possible to find an equivalent form
N(t) = Nat/k2. There are 800 bacteria in a colony at t = 0. There are 1000 bacteria
in the colony
two days later.
a) find r
b) find how many you will have after four days (t=4).
c) Can you set up the problem so that it can be done without a calculator?
d) How long will it take for the population of bacteria to reach 3000? (This part will
probably require a calculator)
In a logistic growth model, the graph will start off looking very similar to an exponential
growth graph, except in the long run, the graph will flatten out and approach a maximum
instead of growing in an unbounded fashion.
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