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) this is the part I’m having the hard time with.

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

for any doubt feel free to ask.

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...

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 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

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.)

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?

8.6343 Q13
Determine the amount of money that will be accumulated in an
account that pays compound interest, given the initial principal
of $28 comma 800 invested at 2.81% annual interest for 7 years
compounded
(a) daily (n=365); =
(b) continuously. =
(Round to the nearest cent as needed.)

At the end of each month, for 24 months, $200 is put into an
account paying 7% annual interest compounded continuously. Find the
future value of this account. Round your answer to the nearest
cent.
How much money must be invested now at 10% interest compounded
continuously so that $120,000 will be available in 5 years? Round
to the nearest cent.
Find the amount of money that accumulates when $470,000 is
placed annually into a non-interest-earning account for 3
years.

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