Question

An initial deposit of $24,000 is made into and account that earns5% compounded continuously. Money is then withdrawn at a constant rate of $4000 a year until the amount in the account is 0. Find the equation for the amount in the account at any time t. What is the amount 0?

Answer #1

Are
you invest in a bank account which pays 6% compounded continuously.
You withdraw money continuously at a rate of $4000 per month. Let B
be the balance in dollars and T be in time year in years. Suppose
you initially start with $3 million.
a)
set up a differential equation for the situation. Include the
initial condition. Do not solve.
b)
find the equilibrium for the differential equation. Is it stable or
unstable?

An initial deposit is made of $12,000 in an account paying 4%
interest compounded continuously. a. How much will the account be
worth in 6 years? b. How long will it take the account to
double?

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/dt =
rS, where r is the annual rate of
interest.
(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...

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...

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...

Problem 1.10 You deposit $5,000 in an account that earns 5%
interest compounded annually in years 1 and 2, and thereafter a
continuous rate δ(t) = 2/(t + 1) (t ≥ 0). What is the value of the
account after 5 years?
Problem 1.11 Suppose an initial investment of $100 grows
according to the accumulated amount function A(t) = 100(1 + 0.05t)
(t ≥ 0). (a) Find the effective rate of interest earned during the
5th year i5. (b) Find...

Suppose you deposit $7000 at 7% interest compounded
continuously. Find the average value of your account during the
first 4 years.

In an effort to save money for early retirement, an
environmental engineering colleague plans
to deposit $1500 every 3 months into a bank account. The first
deposit will be made 3 months
from today and the last deposit will be made at year 10.
A) If the bank’s interest rate is 12% per year compounded
continuously, how much will be in
the account at the end of 10 years? (12.5 points)
B) If the bank’s interest rate is still 12%...

Consider the following deposits made into a savings account that
earns a constant interest compounded annually. 'An' represents the
actual deposits made at the end of year n. 'Pn' represents the
present value of the deposit in year n. The present value 'Pn' of
$750 in year 2 is $667.40. Assuming there are only 4 deposits made,
calculate the total amount in the savings account at the end of
year 4. 'An' in $ (Years 0 through 4): 0 440...

You invest $3500 in an account at interest rate r,
compounded continuously. Find the time required for the amount to
double and triple. (Round your answers to two decimal places.)

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