Question

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*/

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 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* = 5000

1 +

1 |

4 |

(0.0575)

8(4) | |

that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)

*S* = $

Answer #1

Thank you so much sir

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...

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...

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...

Suppose $5000 is invested at an annual interest rate of 4.15% if
compounded continuously.
a) Compute the balance at the end of 16 years.
b) What is the doubling time (round to the nearest year)?
c) What will be the balance at the end of 16 years if computed
quarterly?

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.)

The future value that accrues when $700 is invested at 5%,
compounded continuously, is S(t) = 700e0.05t where t is the number
of years. (Round your answers to the nearest cent.) (a) At what
rate is the money in this account growing when t = 4? $ per year
(b) At what rate is it growing when t = 10? $ per year

Adam deposited $1500 in an account in which interest is
compounded continuously. The annual rate of interest is 2.5 %. How
long does it take for his money to double?

$2000 is deposited with an annual interest of 2% compounded
continuously.
(a) Find the balance of the account in 5 years
(b) How long will it take for the money to become 3 times at
this rate?

Calculate the amount of money that will be in each of the
following accounts at the end of the given deposit period:
Account Holder
Amount
Deposited
Annual
Interest Rate
Compounding
Periods Per Year (M)
Compounding
Periods (Years)
Theodore Logan III
$
1,000
16
%
12
6
Vernell Coles
96,000
12
1
2
Tina Elliot
8,000
8
4
5
Wayne Robinson
118,000
10
3
5
Eunice Chung
32,000
18
2
4
Kelly Cravens
13,000
8
6
4
a.The amount of money...

suppose $5000 is invested in an account at an annual interest
rate of 6.8% compounded continuously. How long (to the nearest
tenth of a year) will it take the investment to double in size?

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