Question

1) When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount *S* present
at time *t*, that is,

* dS*/

(a)Find the amount of money accrued at the end of 9 years when $4000 is deposited in a savings account drawing 5 1/4 $ % annual interest compounded continuously. (Round your answer to the nearest cent.)

(b)In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)

years

(c)Use a calculator to compare the amount obtained in part (a)
with the amount * S* = 4000

(1 + 1/4 (0.0525)^9(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)

*S* = $

2) The rate at which a body cools also depends on its exposed
surface area *S*. If *S* is a constant, then a
modification of (2), given in Section 3.1, is

dT/dt = * kS*(

*T*_{m} = 80° F, then
what is the temperature of the coffee in cup *B* after 30
min? (Round your answer to two decimal places.)

° F

Answer #1

BY THIS WAY, ANSWER OF GIVEN PROBLEM.

When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount S present
at time t, that is,
dS/dt =
rS,
where r is the annual rate of interest.
(a)
Find the amount of money accrued at the end of 8 years when
$5000 is deposited in a savings account drawing 5
3
4
% annual interest compounded continuously. (Round your answer to
the nearest cent.)
$
(b)
In how many years will the...

When interest is compounded continuously, the amount of money
increases at a rate proportional to the amount S present
at time t, that is,
dS/dt =
rS,
where r is the annual rate of interest.
(a)
Find the amount of money accrued at the end of 8 years when
$5000 is deposited in a savings account drawing 5 3/4
% annual interest compounded continuously. (Round your answer to
the nearest cent.)
$
(b) this is the part I’m having the...

Most savings banks advertise that they compound interest
continuously, meaning that the amount S(t) in an
account satisfies the differential equation
dS/dt=rS, where r is the annual
interest rate and t is time measured in years.
a) Show that an annual interest
rate of 8% compounded continuously is the same as an annual
interest rate of 8.33% compounded in years.
b) Show that an annual interest
rate of r compounded continuously is the same as
an annual interest rate of...

How much will $100 grow to if invested at a continuously
compounded interest rate of 8.5% for 9 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 9% for 8.5 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)

How much will $100 grow to if invested at a continuously
compounded interest rate of 7.5% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 7.5 years? (Do
not round intermediate calculation

How much will $100 grow to if invested at a continuously
compounded interest rate of 12% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 12 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =

1)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. How much is our account worth
after 7 years? Round your answer to the nearest penny.
2)We invest $50 per month in an account that pays 3% interest
per year compounded continuously. If we make these deposits for 7
years, what is the present value of this account? Round your answer
to the nearest penny.

The rate of a continuous money flow starts at $800 and increases
exponentially at 3% per year for 5 years. Find the present value
and final amount if interest earned is 4% compounded
continuously.
a) The present value is?
b) The final amount is?
(Do not round until the final answer. Then round to the nearest
cent as needed.)

How long (in years) would $500 have to be invested at 7%,
compounded continuously, to amount to $905? (Round your answer to
the nearest whole number.)

Lee
Holmes deposited $15,600 in a new savings account at 11% interest
compounded annually. At the beginning of 4 years, Lee deposited in
additional $40,600 at 11% interest compounded semiannually. At the
end of 6 years what is the balance in Lee’s account? (Do not round
intermediate calculations. Round your answer to the nearest
cent.)

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