##### A woman invests \$5500 in an account that pays 6% interest per year, compounded c

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A woman invests \$5500 in an account that pays 6% interest per year, compounded continuously.

(a) What is the amount after 2 years? (Round your answer to the nearest cent.)

(b) How long will it take for the amount to be \$9000? (Round your answer to two decimal places.)
yr
Jul 16th, 2015

Use the formula for continuously compounded interest:

A = Pe^(rt)

Where:
A = final amount
P = principal amount
r = interest rate
t = time in years

So:

A = 5500e^(0.06*2)
A = 6201.23

Now, you want to find t when A = 11,000:

11,000 = 5500e^(0.06t)

Divide by 5500:

2 = e^(0.06t)

Take the natural log of both sides and simplify:

ln(2) = ln(e^(0.06t))

ln(2) = 0.06t

ln(2)/0.06 = t

11.55 = t

So it will take 11.55 years.

For the next question, use the formula for non-continuously compounded interest:

A = P(1 + r/n)^(nt)

Where:

A = final amount, after t years
P = principal amount
r = interest rate
n = number of times compounded yearly
t = time, in years

So:

6000 = 3000(1 + 0.065/4)^(4t)

2 = 1.01625^(4t)

ln(2) = ln(1.01625^(4t))

ln(2) = 4t * ln(1.01625)

ln(2)/(4*ln(1.01625)) = t

10.75 = t

So, it will take 10.75 years to reach \$6000.

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Jul 16th, 2015

Jul 16th, 2015

11.55 = t

So it will take 11.55 years.

For the next question, use the formula for non-continuously compounded interest:

10.75 = t

So, it will take 10.75 years to reach \$6000.

Jul 16th, 2015

Jul 16th, 2015

bro...............how you can say wrong answers......

let me check it again

Jul 16th, 2015

i plug in my hw site its saying incorrect

Jul 16th, 2015

Use the formula for continuously compounded interest:

A = Pe^(rt)

Where:
A = final amount
P = principal amount
r = interest rate
t = time in years

So:

A = 5500e^(0.06*2)
A = 6201.23

Now, you want to find t when A = 11,000:

11,000 = 5500e^(0.06t)

Divide by 5500:

2 = e^(0.06t)

Take the natural log of both sides and simplify:

ln(2) = ln(e^(0.06t))

ln(2) = 0.06t

ln(2)/0.06 = t

11.55 = t

So it will take 11.55 years.

Jul 16th, 2015

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Jul 16th, 2015
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Jul 16th, 2015
Dec 9th, 2016
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