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

Algebra
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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

Thank you for the opportunity to help you with your question!

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

can please highlight answer

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

wrong answer

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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