Question

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?

Answer #1

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 Money is then withdrawn at a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?

You have $10,000 to invest for two years. Your bank offers 5%
interest, compounded continuously for funds in a money market
account. Assuming no additional deposits or withdrawals, how much
money will be in that account at the end of two years?

8) If you invest $5,650 in an account paying 8.65% compounded
continuously,
how much money will be in the account at the end of 10 years?
9)You have agreed to pay off an $8,000 loan in 30 monthly
payments of
$298.79 per month. The annual interest rate is 9% on the unpaid
balance.
a) How much of the rst month's payment will apply towards reducing
the principal
of $8,000?
b)What is the unpaid balance (on the principal) after 12 monthly...

1. If a bank advertises a savings account that pays a 6% nominal
interest rate compounded continuously, what is the effective annual
percentage rate?
2. Bank A offers a nominal annual interest rate of 5% compounded
daily, while Bank B offers continuous compounding at a 4.6% nominal
annual rate. If you deposit $3,000 with each bank, what will be the
difference in the two bank account balances after two years?
(Show ALL work and formulas used!)

You invest $50 in a bank account for 5 years, with interest
compounded monthly. How much will you have at the end? compute the
future values for interest rates of 0% to 10%, in 1% increments.
Which of the following accurately displays these calculations? how
would you solve in calculator

You have some money on deposit in a bank account which pays a
nominal APR (or quoted) rate of 8.0944 percent, but with interest
compounded daily (using a 365 day year). Your friend owns a
security which calls for the payment of $10,000 after 27 months.
Your friend's security is just as safe as your bank deposit, and
your friend offers to sell it to you for $8,000 today. If you buy
the security, by how much will the effective...

For how many months do you need to invest your money into a bank
account earning an annual interest rate of 11.5% compounded monthly
if you want to triple your investment? months (Note: Your answer
should be an integer)

You have $84,000 in an account which pays 2.1% compounded
annually. How many additional dollars of interest would you earn
over 9 years if you moved the money to an account earning 3.2%
compounded quarterly? Round to the nearest cent.

You have $67,000 in an account which pays 2.3% compounded
annually. How many additional dollars of interest would you earn
over 8 years if you moved the money to an account earning 3.5%
compounded quarterly? Round to the nearest cent.

You recently received an unexpected monetary gift of
$3,000. Because you took College Algebra, you know that investing
this money in a good bank account will allow your money to grow
exponentially. After visiting several banks in the Allendale area,
you have narrowed it down to two options.
Option 1: At Lake Michigan Credit Union your money will
earn interest rate of 2.05% per year, compounded monthly. Call the
function that models this situation L(t).
Option 2: At Macatawa Bank...

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