Question

Suppose you invest $10,000 in an account which pays 4% interest
per year compounded quarterly. Use the formula F = P(1 +
(i/m))^{mt} where F is the balance in your account t years
into the future, P = the amount of your initial deposit, i is the
annual interest rate, and m is the number of times per year you are
paid interest.

a. Find the function which gives your balance in the account t years after you open it. Use F for the future balance in your account and t for the number of years your account is open. ____________

b. Use your answer from part a to find the year in which you balance has grown to $20,000. ____________

c. Use your answer from part a to find the balance in your account after 25 years. ____________

d. Find dF/dt. ____________

e. Use your answer from part d to find the rate of change in the balance in your account after 25 years. ____________

Answer #1

Suppose you invest $10,000 in an account which pays 4% interest
per year compounded quarterly. Use the formula F = P(1 +
(i/m))mt where F is the balance in your account t years
into the future, P = the amount of your initial deposit, i is the
annual interest rate, and m is the number of times per year you are
paid interest.
a. Find the function which
gives your balance in the account t years after you open
it. Use F...

Suppose you invest $ 800 in an account paying 6 % interest per
year. a. What is the balance in the account after 2 years? How
much of this balance corresponds to "interest on interest"? b.
What is the balance in the account after 30 years? How much of
this balance corresponds to "interest on interest"? a. What is
the balance in the account after 2 years? The balance in the
account after 2 years is $ nothing. (Round...

A person initially deposits $500 in a savings account that pays
interest that pays interest at a rate of 4% per year compounded
continuously. Suppose the person arranges for $10 per week to be
deposited automatically into the savings account.
a) Write a differential equation for P(t), the amount on deposit
after t years and solve.
b) Find the amount on deposit after 5 years.
Hint: dP/dt = 0.04P + 520.

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.

1) Suppose you invest $ 1000in an account paying 6 %interest per
year.
a. What is the balance in the account after 2 years? How much of
this balance corresponds to "interest on interest"?
b. What is the balance in the account after 34 years? How much
of this balance corresponds to "interest on interest"?
What is the balance in the account after 2 years? The balance
in the account (with compounded interest) after 2 years is $___
(Round to...

Suppose $12,500 is invested in an account which offers 3.25%
interest compounded quarterly (4 times a year).
(a) Express the amount A in the account as a function of the
term of the investment t in years.
(b) How much would be in the account in 7 years (assuming non
deposits or withdrawals are made)?
(c) How long will it take for the initial investment to double
(round the nearest tenth of a year)?

You invest in an IRA that has an average interest rate of return
of 7.5% compounded yearly. You open the account with $5000 and
invest $4000 at the end of year3, $7000 at the end of year 6 and
$10000 at the end of year 10. After being invested for 15
years total (since opening the account) what will the IRA's future
value or worth be in dollars? Give your answer in dollars
and no cents. Do not enter units...

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?

(step by step calculation please) Suppose you invest $1000 in an
account paying 6% interest per year. What is the balance in the
account after 3 years? Calculate how much of this balance
corresponds to “interest on interest”

1.You are going to deposit $2,800 in an account that pays .54
percent interest compounded quarterly. How much will you have in 8
years?
2.You have $5,000 and will invest the money at an interest rate
of .21 percent per month until the account is worth $9,800. How
many years do you have to wait until you reach your target account
value?
3.You have just started a new job and plan to save $4,500 per
year for 40 years until...

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