Question

How long (in years) would $500 have to be invested at 7%, compounded continuously, to amount to $905? (Round your answer to the nearest whole number.)

Answer #1

The formula for continuous compounding interest is

A = P(e^{rt} )

where

P = the Principal, which is the same as the starting amount = $500

A = the AFTER amount, which is the same as the ending amount = $905

r = the rate expressed as a decimal, 0.07

t = the number of years it takes for the Principal to become the

AFTER amount. That's the unknown that we want to find.

e = 2.718281828459

So we substitute

A = P(e^{rt} )

905 = 500(e)^{0.07t}

Divide both sides by 500

905 / 500 = (e)^{0.07t}

1.81 = (e)^{0.07t}

The exponential formula A = e^{B} is equivalent to B =
ln(A).

similarly

0.07t = ln(1.81)

t = ln(1.81) / 0.07 = 8.4760977896

t = **8**.4 years

How much will $100 grow to if invested at a continuously
compounded interest rate of 7.5% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 7.5 years? (Do
not round intermediate calculation

How much will $100 grow to if invested at a continuously
compounded interest rate of 12% for 7 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =
How much will $100 grow to if invested at a continuously
compounded interest rate of 7% for 12 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
Future Value =

How much will $100 grow to if invested at a continuously
compounded interest rate of 8.5% for 9 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
How much will $100 grow to if invested at a continuously
compounded interest rate of 9% for 8.5 years? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)

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...

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...

(Compound
value solving for
n)
How many years will the following take?a.
$500
to grow to
$1,039.50
if invested at
5
percent compounded annuallyb.
$35
to grow to
$53.87
if invested at
9
percent compounded annuallyc.
$100
to grow to
$298.60
if invested at
20
percent compounded annuallyd.
$53
to grow to
$78.76
if invested at
2
percent compounded annuallya. How many years will it take
for
$500
to grow to
$1,039.50
if invested at
5
percent compounded annually?
nothing...

What amount would you have if you deposited $7000 a year for 16
years at 7 percent (compounded annually)?
Use the appropriate Time Value of Money table [Exhibit
1-A, Exhibit 1-B, Exhibit 1-C, OR Exhibit
1-D]
(Round your answer to the nearest whole number. Do not
include the comma, period, and "$" sign in your
response.)
Your Answer:

Suppose $5,400 is invested in an account at an annual interest
rate of 3.9% compounded continuously. How long (to the nearest
tenth of a year) will it take the investment to double in size?
Answer:

a. Compute the future value of $1,900 continuously compounded
for 7 years at an annual percentage rate of 9 percent. (Do not
round intermediate calculations and round your answer to 2 decimal
places, e.g., 32.16.) b. Compute the future value of $1,900
continuously compounded for 5 years at an annual percentage rate of
13 percent. (Do not round intermediate calculations and round your
answer to 2 decimal places, e.g., 32.16.) c. Compute the future
value of $1,900 continuously compounded for...

Six years ago you invested certain amount of money at 10 percent
interest, compounded
continuously. Six years later value of your investment was
$18,221. How much did you invest?
a. $10,000 b. $11,500 c. $10,800
d. $11,200 e. none of the above

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 12 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 17 minutes ago

asked 28 minutes ago

asked 47 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago